Details of the Researcher

PHOTO

Fumihiko Nakano
Section
Graduate School of Science
Job title
Professor
Degree

  • 博士（数理科学）（東京大学）

  • 修士（数理科学）（東京大学）

Research History 1

  • 2010/04 - 2020/02
    Gakushuin University

Committee Memberships 2

  • 日本数学階　函数解析学分科会委員

    2013/03 - 2017/03

  • 日本数学会　函数解析学分科会評議員

    2014/03 - 2016/03

Professional Memberships 6

  • 日本数学会

  • 日本物理学会

  • Physical Society of Japan

  • Mathematical Society of Japan

  • Physical Society of Japan

  • Mathematical Society of Japan

︎Show all ︎Show first 5

Research Interests 5

  • Combinatorial Probability

  • Hubbard model

  • Random and quasiperiodic Schroedinger operators

  • Hubbard model

  • Random and quasiperiodic Schroedinger operators

Research Areas 2

  • Natural sciences / Applied mathematics and statistics /

  • Natural sciences / Basic mathematics /

Awards 1

  1. 福原賞

    2011/12　日本数学会関数方程式分科会　シュレーディンガー方程式および関連する数理物理モデルの解析学的研究

Papers 45

  1. Top to random shuffles on colored permutations

    Fumihiko Nakano, Taizo Sadahiro, Tetsuya Sakurai

    Discrete Applied Mathematics　339　336-348　2023/11

    Publisher: Elsevier BV

    DOI： 10.1016/j.dam.2023.06.037 　

    ISSN： 0166-218X

  2. Determinantal formula for generalized riffle shuffle.

    Fumihiko Nakano, Taizo Sadahiro

    Discrete Mathematics　344　(12)　112599-112599　2021

    DOI： 10.1016/j.disc.2021.112599 　

  3. Poisson statistics for beta ensembles on the real line at high temperature Peer-reviewed

    Fumihiko Nakano, Kahn Duy Trinh

    Journal of Statistical Physics　179　(2)　632-649　2020

    Publisher: Springer Science and Business Media LLC

    DOI： 10.1007/s10955-020-02542-y 　

    ISSN： 0022-4715

    eISSN： 1572-9613

  4. A self-adjointness criterion for the Schrödinger operator with infinitely many point interactions and its application to random operators Peer-reviewed

    Masahiro Kaminaga, Takuya Mine, Fumihiko Nakano

    Annales Henri Poincaré(First Online: 12 November 2019)　21　(2)　405-435　2019/11

    Publisher: Springer Science and Business Media LLC

    DOI： 10.1007/s00023-019-00869-1 　

    ISSN： 1424-0637

    eISSN： 1424-0661

  5. A remark on conditions that a diffusion in the natural scale is a martingale Peer-reviewed

    SHIMIZU Yuuki, NAKANO Fumihiko

    Osaka Journal of Mathematics　55　385-391　2018

  6. Gaussian beta ensembles at high temperature : eigenvalue fluctuations and bulk statistics Peer-reviewed

    Fumihiko Nakano, Kahn Duy Trinh

    Journal of Statisical Physics　173　(2)　295-321　2018

  7. Fluctuation of Density of States for 1d Schrodinger Operators Peer-reviewed

    Fumihiko Nakano

    JOURNAL OF STATISTICAL PHYSICS　166　(6)　1393-1404　2017/03

    DOI： 10.1007/s10955-017-1728-8 　

    ISSN： 0022-4715

    eISSN： 1572-9613

  8. On the asymptotic behavior of Bessel-like diffusions Peer-reviewed

    SHIMIZU, Yuuki, NAKANO Fumihiko

    Tsukuba Journal of Mathematics　41　(1)　81-90　2017

  9. Poisson statistics for 1d Schrodinger operators with random decaying potentials Peer-reviewed

    Shinichi Kotani, Fumihiko Nakano

    ELECTRONIC JOURNAL OF PROBABILITY　22　(69)　1-31　2017

    DOI： 10.1214/17-EJP91 　

    ISSN： 1083-6489

  10. A generalization of carries process and riffle shuffles Peer-reviewed

    Fumihiko Nakano, Taizo Sadahiro

    DISCRETE MATHEMATICS　339　(2)　974-991　2016/02

    DOI： 10.1016/j.disc.2015.10.025 　

    ISSN： 0012-365X

    eISSN： 1872-681X

  11. Level Statistics for One-Dimensional Schrodinger Operators and Gaussian Beta Ensemble Peer-reviewed

    Fumihiko Nakano

    JOURNAL OF STATISTICAL PHYSICS　156　(1)　66-93　2014/07

    DOI： 10.1007/s10955-014-0987-x 　

    ISSN： 0022-4715

    eISSN： 1572-9613

  12. A generalization of carries processes and Eulerian numbers

    Fumihiko Nakano, Taizo Sadahiro

    ADVANCES IN APPLIED MATHEMATICS　53　28-43　2014/02

    DOI： 10.1016/j.aam.2013.09.005 　

    ISSN： 0196-8858

    eISSN： 1090-2074

  13. On the level statistics problem for the one-dimensional Schroedinger operator with random decaying potential

    Shinichi Kotani, Fumihiko Nakano

    RIMS Kokyuroku Bessatsu　B45　19-24　2014

    DOI： 10.1007/BF01466772 　

  14. Level statistics for the one-dimensional Schroedinger operators with random decaying potential Peer-reviewed

    KOTANI Shinichi, NAKANO Fumihiko

    Interdisciplinary Mathematical Sciences　17　343-373　2014

  15. A generalization of carries process Peer-reviewed

    FUJITA Takahiko, NAKANO Fumihiko, SADAHIRO Taizo

    Discree Mathematics and Theoretical Computer Science, Proceedin AT　61-69　2014

  16. Hitting Matrix and Domino Tiling with Diagonal Impurities

    Fumihiko Nakano, Taizo Sadahiro

    JOURNAL OF STATISTICAL PHYSICS　151　(6)　1035-1055　2013/06

    DOI： 10.1007/s10955-013-0744-6 　

    ISSN： 0022-4715

  17. A $(-\beta)$-expansion associated to Sturmian sequences

    NAKANO Fumihiko, SADAHIRO Taizo

    Integers　12　(4)　571-600　2012

  18. Domino Tilings with One Diagonal Impurity

    Fumihiko Nakano, Taizo Sadahiro

    FUNDAMENTA INFORMATICAE　117　(1-4)　249-264　2012

    DOI： 10.3233/FI-2012-699 　

    ISSN： 0169-2968

  19. Notes on vertex atlas of Danzer tiling

    中野 史彦, Hiroko Hayashi, Yuu Kawachi, Kazushi Komatsu, Aya Konda, Miho Kurozoe, Fumihiko Nakano, Naomi Odawara, Rika Onda, Akinobu Sugio, Masatetsu Yamauchi

    Nihonkai Journal of Mathematics　22　(1)　49-58　2011

  20. Local move connectedness of domino tilings with diagonal impurities

    Fuminiko Nakano, Hirotaka Ono, Taizo Sadahiro

    DISCRETE MATHEMATICS　310　(13-14)　1918-1931　2010/07

    DOI： 10.1016/j.disc.2010.02.015 　

    ISSN： 0012-365X

  21. A Bijection Theorem for Domino Tilings with Diagonal Impurities

    Fumihiko Nakano, Taizo Sadahiro

    JOURNAL OF STATISTICAL PHYSICS　139　(4)　565-597　2010/05

    DOI： 10.1007/s10955-010-9954-3 　

    ISSN： 0022-4715

  22. INFINITE DIVISIBILITY OF RANDOM MEASURES ASSOCIATED TO SOME RANDOM SCHRODINGER OPERATORS

    Fumihiko Nakano

    OSAKA JOURNAL OF MATHEMATICS　46　(3)　845-862　2009/09

    ISSN： 0030-6126

  23. Remarks on 2-dimensional quasiperiodic tilings with rotational symmetries Peer-reviewed

    Kazuhisa Kato, Kazushi Komatsu, Fumihiko Nakano, Kentaro Nomakuchi, Masatetsu Yamauchi

    HIROSHIMA MATHEMATICAL JOURNAL　38　(3)　385-395　2008/11

    ISSN： 0018-2079

  24. Elementary properties of circle map sequences Peer-reviewed

    NAKANO Fumihiko

    Nihonkai Journal of Mathematics　19　(2)　85-104　2008

    Publisher: Niigata University

    ISSN： 1341-9951

  25. A substitution rule of the Penrose tiling Peer-reviewed

    NAKANO Fumihiko, KOMATSU, Kazushi

    Nihonkai Journal of Mathematics　19　(2)　111-135　2008

  26. Distribution of localization centers in some discrete random systems Peer-reviewed

    Fumihiko Nakano

    REVIEWS IN MATHEMATICAL PHYSICS　19　(9)　941-965　2007/10

    DOI： 10.1142/S0129055X07003176 　

    ISSN： 0129-055X

  27. Finite volume approximation of the Anderson model Peer-reviewed

    Fumihiko Nakano

    JOURNAL OF MATHEMATICAL PHYSICS　48　(4)　42102-42107　2007/04

    DOI： 10.1063/1.2716970 　

    ISSN： 0022-2488

  28. Eigenfunction statistics in the localized Anderson model Peer-reviewed

    Rowan Killip, Fumihiko Nakano

    ANNALES HENRI POINCARE　8　(1)　27-36　2007/02

    DOI： 10.1007/s00023-006-0298-0 　

    ISSN： 1424-0637

  29. The repulsion between localization centers in the Anderson model Peer-reviewed

    Fumihiko Nakano

    JOURNAL OF STATISTICAL PHYSICS　123　(4)　803-810　2006/05

    DOI： 10.1007/s10955-006-9086 　

    ISSN： 0022-4715

  30. The spectrum of Schrodinger operators with Poisson type random potential Peer-reviewed

    K Ando, A Iwatsuka, M Kaminaga, F Nakano

    ANNALES HENRI POINCARE　7　(1)　145-160　2006

    DOI： 10.1007/s00023-005-0245-5 　

    ISSN： 1424-0637

  31. Spin of the ground state and the flux phase problem on the ring Peer-reviewed

    F Nakano

    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL　37　(13)　3979-3987　2004/04

    DOI： 10.1088/0305-4470/37/13/005 　

    ISSN： 0305-4470

  32. Random magnetic fields on line graphs Peer-reviewed

    F Nakano, Y Nomura

    JOURNAL OF MATHEMATICAL PHYSICS　44　(11)　4988-5002　2003/11

    DOI： 10.1063/1.1613377 　

    ISSN： 0022-2488

  33. The Landauer resistivity on quantum wires Peer-reviewed

    M Kaminaga, F Nakano

    JOURNAL OF STATISTICAL PHYSICS　111　(1-2)　339-353　2003/04

    DOI： 10.1023/A:1022265226479 　

    ISSN： 0022-4715

  34. Anderson localization for 2D discrete Schrodinger operators with random magnetic fields Peer-reviewed

    F Klopp, S Nakamura, F Nakano, Y Nomura

    ANNALES HENRI POINCARE　4　(4)　795-811　2003

    DOI： 10.1007/s00023-003-0147-3 　

    ISSN： 1424-0637

  35. Absence of transport in Anderson localization Peer-reviewed

    F Nakano

    REVIEWS IN MATHEMATICAL PHYSICS　14　(4)　375-407　2002/04

    DOI： 10.1142/S0129055X02001211 　

    ISSN： 0129-055X

  36. Spectral properties of quasiperiodic Kronig-Penney model Peer-reviewed

    NAKANO FUMIHIKO

    Tsukuba Journal of Mathematics　26　(2)　205-228　2002

    Publisher: Institute of Mathematics, University of Tsukuba

    ISSN： 0387-4982

  37. The flux phase problem on the ring Peer-reviewed

    F Nakano

    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL　33　(30)　5429-5433　2000/08

    DOI： 10.1088/0305-4470/33/30/311 　

    ISSN： 0305-4470

  38. Absence of transport under a slowly varying potential in disordered systems Peer-reviewed

    F Nakano, M Kaminaga

    JOURNAL OF STATISTICAL PHYSICS　97　(5-6)　917-940　1999/12

    ISSN： 0022-4715

  39. Calculation of the Hall conductivity by Abel limit Peer-reviewed

    F Nakano

    ANNALES DE L INSTITUT HENRI POINCARE-PHYSIQUE THEORIQUE　69　(4)　441-455　1998/10

    ISSN： 0246-0211

  40. Calculation of the Hall conductivity by adiabatic approximation Peer-reviewed

    NAKANO Fumihiko

    Journal of Mathematical Sciences University of Tokyo　4　(2)　351-371　1997

    Publisher: The University of Tokyo

    ISSN： 1340-5705

  41. Analysis of Schoedinger eguations in magnetic fields

    NAKANO FUMIHIKO

    University of Tokyo　1996/03

  42. Asymptotics of Heavy Molecules in High Magnetic Fields Peer-reviewed

    NAKANO Fumihiko

    Journal of Methematical Sciences, University of Tokyo　3　(2)　247-270　1996

    Publisher: The University of Tokyo

    ISSN： 1340-5705

  43. The thermodynamic limit of the magnetic Thomas-Fermi energy Peer-reviewed

    NAKANO Fumihiko

    Journal of Mathematical Sciences, University of Tokyo　3　(3)　713-722　1996

    Publisher: The University of Tokyo

    ISSN： 1340-5705

  44. Semiclassical Analysis of Schroedinger Operators with Coulomb-like singular potentials Peer-reviewed

    NAKANO Fumihiko

    Journal of Mathematical Sciences, University of Tokyo　1　(3)　589-615　1994

  45. Semiclassical analysis of Schr\"odinger operators with Coulomb-like singular potentials Peer-reviewed

    NAKANO Fumihiko

    University of Tokyo　1993/03

Show all ︎Show first 5

Misc. 16

  1. Density of states and level statistics for 1d Schr\"odinger operators

    NAKANO Fumihiko

    Kokyuroku　2010　93-104　2016/12

  2. On the generalized carries process

    NAKANO Fumihiko

    Kokyuroku　1998　161-170　2016/07

  3. Domino tilings of Aztec rectangles with connected holes

    Ishikawa Masao, Nakano Fumihiko, Sadahiro Taizo, Tagawa Hiroyuki

    RIMS Kokyuroku　1992　114-125　2016

  4. On the level statistics for 1 dimensional random Schroedinger operators

    NAKANO Fumihiko

    RIMS Kokyuroku　1969　93-100　2015

  5. Limit of Sine$_{\beta}$ and Sch$_{\tau}$ processes

    NAKANO Fumihiko

    RIMS Kokyuroku　1970　83-89　2015

  6. On some aspects of $(-\beta)$-expansion

    NAKANO Fumihiko

    RIMS Kokyuroku　1725　92-105　2011

  7. A remark on distribution of eigenfunctions of the Anderson model on the Bethe lattice

    NAKANO Fumihiko

    RIMS Kokyuroku,　1600　147-151　2008/05

  8. Distribution of eigenfunctions in the Anderson model

    NAKANO Fumihiko

    Kokyuroku, Hokkaido University　122　1-9　2007/08

  9. Distribution of eigenfunctions in Anderson model

    NAKANO Fumihiko

    RIMS Kokyuroku,　1563　43-51　2007/06

  10. On the estimate of number of negative eigenvalues of the Schroedinger operator

    NAKANO Fumihiko

    RIMS Kokyuroku,　1402　69-75　2004/11

  11. Anderson localization for a random flux model

    NAKANO Fumihiko

    RIMS Kokyuroku,　1386　176-183　2004/07

  12. Flux phase and Spin problem on the ring

    NAKANO Fumihiko

    RIMS Kokyuroku　1364　108-117　2004/04

  13. On the ferromagnetism in the t-t' Hubbard model

    NAKANO Fumihiko

    Meeting abstracts of the Physical Society of Japan　53　(1)　641-641　1998/03/10

    Publisher: The Physical Society of Japan (JPS)

    ISSN： 1342-8349

  14. Semiclassical analysis of Schr\"odinger operators with Coulomb-like singular potentials

    NAKANO Fumihiko

    RIMS Kokyuroku, "Spectra, scattering theory and related topics"　873　68-86　1994

  15. 負の特異点のあるポテンシャルをもつシュレーディンガー方程式の準古典解析

    中野 史彦

    1993

  16. Clock statistics for 1d Schr\"odinger operators

    Victor Chulaevsky, Fumihiko Nakano

Show all ︎Show first 5

Books and Other Publications 1

  1. 『二項係数について』数学セミナー2020年7月号

    中野史彦

    日本評論社　2020/06

Presentations 66

  1. 1次元ランダムシュレーディンガー作用素の固有値・固有関数のスケーリング極限について Invited

    中野史彦

    偏微分方程式姫路研究集会　2021/03/05

  2. Statistics in Random Schroedinger Operators Invited

    Nancy-Tohoku Meeting　2021/01/26

  3. キャリーズプロセスの性質と応用

    中野史彦

    確率論セミナー　2020/12/18

  4. １次元ランダムシュレーディンガー作用素の固有値・固有関数のスケーリング極限について Invited

    中野史彦

    応用数学セミナー　2020/10/29

  5. 1次元ランダムシュレーディンガー作用素の固有値・固有関数のスケーリング極限について Invited

    中野史彦

    日本数学会 2020年度秋季総合分科会特別講演　2020/09/22

  6. 一般化キャリーズプロセスとリフルシャッフル Invited

    中野史彦

    確率論月曜セミナー　2020/02/03

  7. Scaling limit of eigenfunctions for 1d random Schr\"odinger operators Invited

    2020/01/15

  8. １次元ランダムシュレーディンガー作用素の固有値・固有関数のスケーリング極限について Invited

    中野史彦

    阪大確率論セミナー　2019/10/28

  9. Asymptotic behavior of eigenfunctions of 1d random Schroedinger operators Invited

    2019

  10. Asymptotic behavior of eigenfunctions of 1d random Schroedinger operators International-presentation Invited

    NAKANO Fumihiko

    Seminar at Tsinghua University　2018/11/05

  11. Asymptotic behavior of eigenfunctions for random Schroedinger operators Invited

    NAKANO Fumihiko

    2018/10/27

  12. Spectral property of large but finite random systems Invited

    NAKANO Fumihiko

    Summer School on Probability Theory　2018/08/27

  13. Density of states and level statistics for 1d Schroedinger operators Invited

    NAKANO Fumihiko

    Seminar on Mathematical Physics　2018/07/18

  14. Density of states and level statistics for 1d Schroedinger operators International-presentation Invited

    NAKANO Fumihiko

    Random matrices and their applications　2018/05/21

  15. Remarks on generalized carries process and riffle shuffle Invited

    NAKANO Fumihiko

    2018/03/26

  16. Remarks on generalized carries process and riffle shuffle Invited

    NAKANO Fumihiko

    Workshop on Random Matrices, determinant processes, and their related topics, in Beppu 2018　2018/03/09

  17. Generalized carries process and riffle shuffles International-presentation Invited

    NAKANO Fumihiko

    Algebraic and Enumerative Combinatorics in Okayama　2018/02/19

  18. Level statistics for 1 dimensional Schroedinger Operators International-presentation Invited

    NAKANO Fumihiko

    Spectral, Scattering Theory and Related Topics　2017/12/07

  19. Some remarks on a generalized caries process International-presentation Invited

    NAKANO Fumihiko

    Workshop“Number Theoretical Aspects of Tilings and Dynamics”　2017/11/23

  20. Density of states and level statistics for 1d Schroedinger operators Invited

    NAKANO Fumihiko

    Okayama-Hiroshima joint seminar on Analysis and Probability 2017　2017/02/20

  21. Density of states and level statistics for 1d Schroedinger operators

    NAKANO Fumihiko

    Colloqium at Kumamoto University　2017/01/25

  22. Generalized carries process and riffle shuffles Invited

    NAKANO Fumihiko

    Concentrated Lecture at Kumamoto University　2017/01/23

  23. Density of states and level statistics for 1d Schroedinger operators International-presentation Invited

    NAKANO Fumihiko

    Analysis on Fractals and Graphs Workshop　2016/12/28

  24. On the asymptotic behavior of the Bessel-like diffusion Invited

    NAKANO Fumihiko

    Spectrum of random operators and related topics　2016/12/15

  25. Poisson statistics for the Gaussian beta ensembles at high temperature International-presentation

    NAKANO Fumihiko

    Schrodinger operators and dynamics　2016/11/15

  26. Generalized Carries Process and Riffle Shuffles Invited

    NAKANO Fumihiko

    Kyushu Probability Seminar　2016/08/26

  27. Density of states and level statistics for 1d Schroedinger operators International-presentation Invited

    NAKANO Fumihiko

    Beta ensembles: Universality, Integrability and Asymptotics　2016/04/12

  28. Generalized carries process and riffle shuffles International-presentation Invited

    NAKANO Fumihiko

    Fractals and Numerations Substitutions and continued fractions　2016/03/11

  29. Density of states and level statistics for 1d Schroedinger operators International-presentation Invited

    NAKANO Fumihiko

    Colloqium at University de Champagne-Ardenne　2016/03/07

  30. Generalized carries process and riffle shuffles International-presentation Invited

    NAKANO Fumihiko

    Sino-Japanese workshop on Dynamical Systems and Fractals　2015/12/27

  31. Poisson statistics for 1d Schroedinger operators with random decaying potential International-presentation Invited

    NAKANO Fumihiko

    Spectra of random operators and related topics　2015/12/10

  32. Theory of Anderson localization for d dimensions International-presentation Invited

    NAKANO Fumihiko

    Seminar at Tsinghua University　2015/11/19

  33. Density of states and level statistics for 1d Schroedinger operators International-presentation Invited

    NAKANO Fumihiko

    Seminar at Tsinghua University　2015/11/12

  34. Generalized carries process and riffle shuffles Invited

    NAKANO Fumihiko

    Strongly aperiodic tilings and related topics　2015/10/21

  35. Level statistics and Density of states of 1 d Schroedinger operator Invited

    NAKANO Fumihiko

    Mathematics of quantum fields and related topics　2015/10/15

  36. Algebraic combinatoricsge

    中野 史彦

    代数的組合せ論勉強会　2015/10/15

  37. Algebraic combinatorics

    中野 史彦

    代数的組合せ論勉強会　2015/08/07

  38. Algebraic combinatorics Invited

    中野 史彦

    代数的組合せ論勉強会　2015/06/19

  39. Level statistics for 1-dimensional Schr\"odinger operator and beta-ensemble International-presentation Invited

    NAKANO Fumihiko

    Mathematics of Novel Materials　2015/06/03

  40. Level statistics of 1-dim Schroedinger operators and beta - ensemble International-presentation Invited

    NAKANO Fumihiko

    Almost-Periodic and Other Ergodic Problems　2015/04/10

  41. Limit of Sine$_{\beta}$ and Sch$_{\tau}$-processes Invited

    NAKANO Fumihiko

    Random Matrices, determinantal processes, and inte- grable probability　2015/03/06

  42. Level statistics for random Schr\"odinger operators, 1, 2 Invited

    NAKANO Fumihiko

    2015/02/16

  43. Level statistics for 1-dimensional Schr\"odinger operator and beta-ensemble Invited

    NAKANO Fumihiko

    2015/01/14

  44. Limit of Sine$_{\beta}$ and Sch$_{\tau}$-processes Invited

    NAKANO Fumihiko

    Spectra of random operators and related topics　2015/01/08

  45. Level statistics for 1-dimensional Schr\"odinger operator and beta-ensemble International-presentation Invited

    NAKANO Fumihiko

    Lame Conference on "The Mathematics of Quantum Disordered System"　2014/12/15

  46. The level statistics for one-dimensional Schroedinger operator International-presentation Invited

    NAKANO Fumihiko

    Spectra of random operators and related topics　2014/12/05

  47. Level statistics for 1-dimensional Schr\"odinger operator and beta-ensemble

    NAKANO Fumihiko

    2014/11/01

  48. A generalization of carries process Invited

    NAKANO Fumihiko

    2014/10/28

  49. A generalization of carries process International-presentation Invited

    NAKANO Fumihiko

    Tiling dynamics and related topics　2014/09/17

  50. A generalization of carries process Invited

    NAKANO Fumihiko

    2014/06/19

  51. １次元ランダムシュレーディンガー作用素の準位統計について Invited

    中野 史彦

    KPZ 勉強会　2014/04/26

  52. The level statistics for one-dimensional Schroedinger operator International-presentation Invited

    NAKANO Fumihiko

    Sino-Japanese workshop on Fractals and Dynamical Systems　2013/12/25

  53. A generalization of carries process International-presentation Invited

    NAKANO Fumihiko

    Geometric aspects in probability and analysis　2013/09/14

  54. The level statistics for one-dimensional Schroedinger operator International-presentation

    NAKANO Fumihiko

    QMath 12　2013/09/10

  55. １次元ランダムシュレーディンガー作用素の準位統計について Invited

    中野 史彦

    東京確率論セミナー　2013/06/10

  56. A generalization of carries process International-presentation Invited

    NAKANO Fumihiko

    Markov chains on graphs and related topics　2013/02/12

  57. Thomas-Fermi理論入門 Invited

    中野 史彦

    信州大学集中講義　2013/01/21

  58. Carry Process and Amazing Matrix

    NAKANO Fumihiko

    2012/12/20

  59. 不純物を含むダイマーモデルについて Invited

    中野 史彦

    置換行列の数理科学　2012/12/18

  60. Level statistics of 1 dimensional random Schroedinger operators International-presentation Invited

    NAKANO Fumihiko

    Spectra of random operators and related topicsect　2012/12/05

  61. １次元ランダムシュレーディンガー作用素の準位統計について

    中野 史彦

    微分方程式と数理物理　2012/11/03

  62. Kenyon-Wilson 理論とダイマーモデルへの応用 Invited

    中野 史彦

    CREST セミナー 東北大学　2012/07/26

  63. エルゴード的シュレーディンガー作用素のスペクトル理論 Invited

    中野 史彦

    新潟大学 集中講義　2012/06/25

  64. １次元ランダムシュレーディンガー作用素の準位統計について Invited

    中野 史彦

    幾何学的偏微分方程式に対する保存則と正則性特異性の研究　2012/06/13

  65. The level statistics of one-dimensional Schroedinger operator with random decaying potential International-presentation Invited

    NAKANO Fumihiko

    Mathematics of quantum disordered systems”, Univ.Paris13　2012/05/28

  66. Kenyon-Wilson 理論とその応用について Invited

    中野 史彦

    東京力学系セミナー、文京学院大学　2012/05/19

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Research Projects 26

  1. ランダムシュレーディンガー作用素及びランダム行列の準位統計

    中野 史彦

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業 基盤研究(C)

    Category: 基盤研究(C)

    Institution: 東北大学

    2020/04/01 - 2025/03/31

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    (1) ランダムシュレーディンガー作用素(RSO)の固有関数のスケーリング極限：減衰ポテンシャルを持つ１次元ランダムシュレーディンガー作用素において，その固有関数のスケーリング極限を調べる研究を数年前から続けているが，固有値の満たす点過程の分布極限がポアソン過程であるときに，ある程度一般的な枠組みの下で，固有値とその局在中心のペアのなす点過程の分布極限もまた（直積空間上の）ポアソン過程になることを示した．また、一般的な枠組みの中で、エネルギーの局所的な点過程の強度測度が大域的点過程の分布を与えることを示した。 (2) RSOの固有値の極値統計：減衰ポテンシャルを持つd次元ランダムシュレーディンガー作用素において，その状態密度を求めた. また, その有限体積版において，最大固有値から数えて任意の有限個をとってスケーリングして得られる点過程を考える. ランダムポテンシャルの分布においてある程度一般的な仮定の下において，この点過程が非一様なポアソン過程に分布収束することを示した． (3) RSOの固有値のゆらぎ：減衰ポテンシャルを持つ１次元ランダムシュレーディンガー作用素において，そのlinear statisticsを複数の解析関数について考え，そのゆらぎの同時分布が多次元ガウス分布に分布収束することを示した.また， linear statisticsの期待値の漸近公式を求めた． (4)Top to random shuffle : 色付き置換群上のTop to random shuffleにおいて，推移確率行列の固有値とその多重度，原始ベキ等元の導出を行った．また，混合時間の漸近評価を行い，それがカットオフ現象を示すことを示した．

  2. Level statistics for random Schroedinger operators Competitive

    NAKANO Fumihiko

    Offer Organization: JSPS

    System: JSPSGrant

    2014/04 - 2019/03

  3. A generalization of carries process

    Sadahiro Taizo, ISHIKAWA Masao, NAKANO Fumihiko, FUJITA Takahiko

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (C)

    Institution: Tsuda College

    2014/04/01 - 2018/03/31

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    When we add randomly generated integers, the sequence of the carries can be considered as a Markov chain. The transition probability matrix of this chain exhibits some remarkable properties, the eigenvalues and eigenvectors can be representd explicitly. We generalize this Markov chain and obtained an explicit formula which represents the eigenvalues and eigenvectors. We found a relation between this Markov chain and the riffle shuffle on the colored permutation groups.

  4. Distribution of eigenvalues of random operators and related limit theorems

    MINAMI Nariyuki, NAKANO Fumihiko, UEKI Naomasa

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (C)

    Institution: Keio University

    2014/04/01 - 2018/03/31

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    (1) 1-dimensional Schroedinger operator H with decaying white noise potential is considered, and its spectral properties are determined when the decaying factor is square integrable. Also, the property of a part of the spectrum of H is determined when the decaying factor is not square integrable. (2) Based on a mathematical model which incorporates a hypothesis that adult males and females are mildly segregated in their social life, it is shown that a condition is ready for the 2013 rubella outbreak in Japan. By another mathematical model, possible consequences of the rubella vaccination limited to schoolgirls were shown. (3) A stochastic model is constructed in order to clarify the notion of "generation interval" in infectious disease epidemiology.

  5. 定常点過程論の枠組みによるランダム作用素のスペクトル統計の研究 Competitive

    南 就将

    Offer Organization: 日本学術振興会

    System: 科学研究費 基盤研究C

    2010/04 - 2014/03

  6. Level statistics for random Schroedinger operators Schroedinger operators S Competitive

    NAKANO Fumihiko

    Offer Organization: JSPS

    2010/04 - 2014/03

  7. Spectral and scattering theory for Schroedinger equations Competitive

    Shu Nakamura

    System: JSPS Grant

    2009/04 - 2014/03

  8. シュレーディンガー作用素に対するスペクトル漸近解析 Competitive

    田村 英男

    Offer Organization: 日本学術振興会

    System: 科学研究費 基盤研究B

    2009/04 - 2013/03

  9. 量子場相互作用系の非摂動的スペクトル解析 Competitive

    廣島 文生

    Offer Organization: 日本学術振興会

    System: 科学研究費 基盤研究B

    2008/04 - 2011/03

  10. Spectra of random Schroedinger operators Competitive

    NAKANO Fumihiko

    Offer Organization: JSPS

    System: JSPS Grant

    Category: Grant-in-Aid for Scientific Research (C)

    Institution: Kochi University

    2006/04 - 2010/03

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    We consider the distribution of eigenvalue and eigenfunction on the localized region of the random Schroednger operator on d-dimensional square lattice. We showed that, (1) they are uniformly distributed, as a whole, (2) they obey Poisson distribution in the natural scaling limit, and (3) they are repulsive under smaller scaling. Moreover, if we have Minami's estimate, the same results also hold for the random Schrodeinger operaors on the continuum.

  11. Classification of quasi-periodic structure with local configurations of Archimedes tiling

    KOMATSU Kazushi, AKIYAMA Shigeki, GOTO Satoru, KATO Kazuhisa, NOMAKUCHI Kentaro, NAKANO Fumihiko

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (C)

    Institution: Kochi University

    2008 - 2010

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    We study details of local configurations around vertices of non-periodic tilings. We can construct an uncountable family of non-periodic tilings with 7-fold rotational symmetry which have just three kinds of local configurations around vertices in Archimedean tilings. These non-periodic tilings have singular local configurations around vertices. The Danzer tiling with 7-fold rotational symmetry has a singular local configurations around vertices. This implies that the Danzer tiling with 7-fold rotational symmetry cannot be obtained as a limit of sequence of canonical tilings.

  12. Asymptotic analysis for spectral and scattering theory Competitive

    TAMURA Hideo

    Offer Organization: JSPS

    System: JSPS Grant

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Okayama University

    2006/04 - 2009/03

  13. Fluctuation of spectra for random operators Competitive

    MINAMI Nariyuki

    Offer Organization: JSPS

    System: JSPS Grant

    2005/04 - 2008/03

  14. Analysis for pre-fractal structures in guasiperiodic filings

    KOMATSU Kazushi, NOMAKUCHI Kentaro, NAKANO Fumihiko, AKIYAMA Shigeki

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (C)

    Institution: Kochi University

    2006 - 2007

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    The summary of research results is as follows 1. We construct a sequentially compact spam of patches in 2 and higher dimensional oases By using this constnction, we analyze certain symmetries of tilings obtained by substitution rules we give explicitly the construction of tilings with rotational symmetries in some examples(a Penrose tiling, an Ammann-Beenker tiling a Danzer tiling). 2. We give a mathematical model of n-membered ringed hydrocarbon molecules, and study the topology of a configuration space of the model. Assuming requited conditions for ringed molecules, we prove that its configuration space is diffeomorphic to (n-4)-dimensional sphere for n> 4. This result gives an appropriate explanation of the configuration space of n-membered ringed hydrocarbon molecules when n= 5, 6. 3. We consider the point process composed of the eigenvalues and corresponding localization centers, and showed that in the infinite volume limit it converges to the Poisson point process. 4. We studied the coding of 1-dimensional irrational rotation with arbitray decomposition of the unit interval. The coded sequence has recursively renewable structure, and we then classify when this procedure is described by stationaly process. It tured out that this happens when and only when all decomposition points, the initial value and the speed of rotations are in the same real quadratic field. 5. We studied the points on the boundary of SRS region whether they always produces eventually periodic orbits or not. Remarkably we prove that this periodicity is valid in the case of golden mean. This study extends to recent further researches on discretized rotation having self-indudng structures. 6. We obtain a theorem on stable unextendibility of R-vector bundles over (2n+1)-dimensional standard lens space mod 3 improving some known results.

  15. 対称マルコフ過程の大偏差原理とディリクレ形式 Competitive

    竹田 雅好

    Offer Organization: 日本学術振興会

    System: 科学研究費 基盤研究C

    2003/04 - 2006/03

  16. Quasiperiodic and random Schroedinger equations Competitive

    NAKANO Fumihiko

    Offer Organization: JSPS

    System: JSPS Grant

    2003/04 - 2005/03

  17. 可換及び非可換ブロッホ理論 Competitive

    砂田 利一

    Offer Organization: 日本学術振興会

    System: 科学研究費 基盤研究A

    2001/04 - 2005/03

  18. Characterizations of the quasi-periodicity in the quasi-crystal structure

    KOMATSU Kazushi, HEMMI Yutaka, SHIMOMURA Katsumi, NAKANO Fumihiko, SADAHIRO Taizo

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (C)

    Institution: Kochi University

    2003 - 2005

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    The summary of research results is as follows. 1.The Ammann-Beenker tilings are quasiperiodic tilings of the plane, which is constructed by using the Ammann's matching rules. We show that the Ammann-Beenker tilings can be composed by an automaton with 4 states, and note some results concerning composition sequences from the viewpoint of symbolic dynamics. 2.Under the assumption that the restriction map of the orthogonal projection to a lattice is injective, we determine when two tilings obtained by the projection method belong to the same isomorphism class. As its application we have uncountably many isomorphism classes of quasiperiodic tilings by the projection method. 3.We prove that the tangent bundle of the (2n+1)-dimensional mod 3 standard lens space is stably extendible to the (2m+1)-dimensional mod 3 standard lens space for every m=n or m>n if and only if n=0,3 or 0<n<3 $. 4.We obtain a theorem on stable unextendibility of R-vector bundles over lens space improving some results, study relations between stable extendibility and span of vector bundles over lens space, and prove that the complexification is extendible for every m>n if and only if n=0,5 or 0<n<5, and prove that the complexification of the tensor product is extendible for every m>n if and only if 0<n<13 or n=0,13,15. 5.We study the structure of the Penrose tiling constructed by the matching rule, and a substitution rule, which gives us the local configuration of the tiles, the elementary proofs of the aperiodicity, the locally isomorphic property, the uncountability and the fact that all obtained by the matching rule can be constructed via the up-down generation.

  19. ホイヘンス作用素の研究 Competitive

    島倉 紀夫

    Offer Organization: 日本学術振興会

    System: 科学研究費 萌芽研究

    2002/04 - 2003/03

  20. Schroedinger equation with a magnetic fields Competitive

    NAKANO Fumihiko

    Offer Organization: JSPS

    System: JSPS Grant

    2000/04 - 2002/03

  21. 離散幾何解析学の基礎的研究と応用 Competitive

    砂田 利一

    Offer Organization: 日本学術振興会

    System: 科学研究費 基盤研究A

    1998/04 - 2001/03

  22. Ferromagnetism for the Hubbard model Competitive

    NAKANO Fumihiko

    Offer Organization: JSPS

    System: Research for abroad

    1998/09 - 2000/08

  23. 反応拡散方程式系の特異摂動解と集中現象 Competitive

    高木 泉

    Offer Organization: 日本学術振興会

    System: 科学研究費 基盤研究B

    1997/04 - 2000/03

  24. Schroedinger equations with magnetic fields Competitive

    NAKANO Fumihiko

    Offer Organization: JSPS

    System: JSPS Grant

    1997/04 - 1999/03

  25. Random and quasiperiodic Schroedinger equation Competitive

    1996 -

  26. Ferromagnetism in the Hubbard model Competitive

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