Zero processes of random analytic functions

• Project/Area Number: 18540130
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kyushu University
• Principal Investigator: SHIRAI Tomoyuki Kyushu University, 大学院・数理学研究院, 教授 (70302932)
• Project Period (FY): 2006 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥4,250,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥750,000); Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
• Keywords: 確率論 / フェルミオン点過程 / 大偏差原理 / Ginibre点過程 / ランダム行列 / α行列式 / 零点過程 / 行列式点過程 / ジニブル点過程 / ランダウレヴェル / 全域木 / Ginibreランダム場

Research Abstract

The zeros of a random polynomial (or a random analytic function) form a random point configuration in the complex plane. This is different from the so-called Poisson random configuration which is obtained by uniformly random sampling in the complex plane, and their points are mutually repulsive nature while Poisson random points often form weak clustering. We clarify the difference of these point configurations.

Research Products

• [Journal Article] A remark on monotonicity for the Glauber dynamics on finite graphs (2010)
  • Author(s): Tomoyuki Shirai
  • Journal Title: Proceedings of the Japan Academy 86(Refereed) Pages: 33-37
  • NAID: 120005227439
• [Journal Article] A remark on monotonicity for the Glauber dynamics on finite graphs (2010)
  • Author(s): T.Shirai
  • Journal Title: Proceedings of the Japan Academy 86 Pages: 33-37
  • NAID: 120005227439
  • Peer Reviewed
• [Journal Article] Variance of randomized values of Riemann's zeta function on the critical line (2008)
  • Author(s): Tomoyuki Shirai
  • Journal Title: RIMS Kokyuroku 1590(Not refereed) Pages: 86-96
• [Journal Article] Joint distribution of the cover time and the last visited point of finite Markov chains (2008)
  • Author(s): Takuya Ohwa, Tomoyuki Shirai
  • Journal Title: Kyushu Journal of Mathematics 62(Refereed) Pages: 281-292
  • NAID: 110006648028
• [Journal Article] Variance of the linear statistics of the Ginibre random point field (2008)
  • Author(s): Hirohumi Osada, Tomoyuki Shirai
  • Journal Title: RIMS Kokyuroku Bessatsu B6(Refereed) Pages: 193-200
• [Journal Article] Variance of the linear statistics of the Ginibre random point field (2008)
  • Author(s): Hirohumi Osada and Tomoyuki Shirai
  • Journal Title: RIMS Kokyuroku Bessatsu B6 Pages: 193-200
  • Peer Reviewed
• [Journal Article] Joint distribution of the cover time and the last visited point of inite Markov chains (2008)
  • Author(s): Takuya Ohwa and Tomoyuki Shirai
  • Journal Title: Kyushu Journal of Mathematics 62 Pages: 281-292
  • Peer Reviewed
• [Journal Article] Variance of the linear statistics of the Ginibre random point field (2008)
  • Author(s): H. Osada, T. Shirai
  • Journal Title: RIMS Kokyuroku Bessatsu B6 Pages: 193-200
  • Peer Reviewed
• [Journal Article] Joint distribution of the cover time and the last visited point of finite Markov chains (2008)
  • Author(s): T. Ohwa, T. Shirai
  • Journal Title: Kyushu Journal of Mathematics 62 Pages: 281-292
  • NAID: 110006648028
  • Peer Reviewed
• [Journal Article] Remarks on the positivity of alpha-determinants (2007)
  • Author(s): Tomoyuki Shirai
  • Journal Title: Kyushu Journal of Mathematics 61(Refereed) Pages: 169-189
  • NAID: 130000063189
• [Journal Article] Remarks on the positivity of alpha-determinants (2007)
  • Author(s): Tomoyuki Shirai
  • Journal Title: Kyushu Journal of Mathematics 61 Pages: 169-189
  • NAID: 130000063189
  • Peer Reviewed
• [Journal Article] Large deviations for the fermion point process associated with the exponential kernel (2006)
  • Author(s): Tomoyuki Shirai
  • Journal Title: Journal of Statistical Physics 123(Refereed) Pages: 615-629
• [Journal Article] Large deviations for the fermion point process associated with the exponential kernel (2006)
  • Author(s): Tomoyuki Shirai
  • Journal Title: Journal of Statistical Physics 123 Pages: 615-629
  • Peer Reviewed
• [Journal Article] Non-bipartiteness of graphs and the upper bounds of Dirichlet forms (2006)
  • Author(s): Yusuke Higuchi, Tomoyuki Shirai
  • Journal Title: Potential Analysis 25 Pages: 259-268
• [Presentation] Determinantal point processes associated with certain reproducing kernels (2010)
  • Author(s): T.Shirai
  • Organizer: The First CREST-SBM International Conference" Random Media"
  • Place of Presentation: Sendai International Center, Sendai, Japan
  • Year and Date: 2010-01-25
• [Presentation] Determinantal point processes associated with certain reproducing kernels (2010)
  • Author(s): Tomoyuki Shirai
  • Organizer: The First CREST-SBM International Conference "Random Media"
  • Place of Presentation: Sendai International Center, Sendai, Japan
• [Presentation] Randomized values of Riemann's zeta function on the critical line (2009)
  • Author(s): T. Shirai
  • Organizer: The 3^<rd> Cheongju Workshop on Infinite Dimensional Analysis and Quantum Probability
  • Place of Presentation: Chungbuk University
  • Year and Date: 2009-01-12
• [Presentation] Ginibre-type determinantal processes (2009)
  • Author(s): Tomoyuki Shirai
  • Organizer: VIIIth Stochastic Analysis on Large Scale Interacting Systems
  • Place of Presentation: University of Tokyo
• [Presentation] Randomized values of Riemann's zeta function on the critical line (2009)
  • Author(s): Tomoyuki Shirai
  • Organizer: The 3rd Cheongju Workshop on Infinite Dimensional Analysis and Quantum Probability
  • Place of Presentation: Chungbuk University
• [Presentation] Random analytic functions and determinantal point processes (2008)
  • Author(s): Tomoyuki Shirai
  • Organizer: RIMS共同研究「L関数の値分布に関係する数論的な諸関数の研究」
  • Place of Presentation: RIMS, Kyoto
• [Presentation] Random analytic functions and determinantal point processes, RIMS共同研究「L関数の値分布に関係する数論的な諸関数の研究」 (2008)
  • Organizer: RIMS
  • Place of Presentation: Kyoto
• [Presentation] Variance of randomized values of Riemann's zeta function on the critical line (2007)
  • Author(s): T. Shirai
  • Organizer: Number Theory and Probability Theory
  • Place of Presentation: 国際高等研究所
  • Year and Date: 2007-10-16
• [Presentation] Determinantal processes associated with non-symmetric kernel (2007)
  • Author(s): Tomoyuki Shirai
  • Organizer: Stochastic Analysis on Large Scale Interacting Systems
  • Place of Presentation: Nishijin Plaza, Fukuoka
• [Presentation] Variance of randomized values of Riemann's zeta function on the critical line (2007)
  • Author(s): Tomoyuki Shirai
  • Organizer: Workshop "Number theory and probability theory"
  • Place of Presentation: RIMS-IIAS, Kyoto
• [Presentation] Variance of randomized values of Riemann's zeta function on the critical line, Workshop "Number theory and probability theory" (2007)
  • Organizer: RIMS-IIAS
  • Place of Presentation: Kyoto
• [Presentation] Determinantal processes associated with non-symmetric kernel, "Stochastic Analysis on Large Scale Interacting Systems" (2007)
  • Organizer: Nishijin Plaza
  • Place of Presentation: Fukuoka