Diffusion method in random matrix theory

被引：7
|
作者：
Grela, Jacek [1 ,2 ]
机构：
[1] Jagiellonian Univ, M Smoluchowski Inst Phys, PL-40348 Krakow, Poland
[2] Jagiellonian Univ, Mark Kac Complex Syst Res Ctr, PL-40348 Krakow, Poland
来源：
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2016年 / 49卷 / 01期
关键词：
random matrix theory; characteristic polynomials; diffusion equation; CHARACTERISTIC-POLYNOMIALS; EQUATION;
D O I：
10.1088/1751-8113/49/1/015201
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We introduce a calculational tool useful in computing ratios and products of characteristic polynomials averaged over Gaussian measures with an external source. The method is based on Dyson's Brownian motion and Grassmann/ complex integration formulas for determinants. The resulting formulas are exact for finite matrix size N and form integral representations convenient for large N asymptotics. Quantities obtained by the method are interpreted as averages over standard matrix models. We provide several explicit and novel calculations with special emphasis on the beta = 2 Girko-Ginibre ensembles.
引用
收藏
页数：18
相关论文
共 50 条
  • [31] Simplified Setting Method of Distance Backup Protection Based on Random Matrix Theory
    Zhao, Zihan
    Yang, Xiangfei
    Xiang, Bo
    Chen, Hongjing
    Tian, Fengxun
    Yi, Jianbo
    2020 5TH ASIA CONFERENCE ON POWER AND ELECTRICAL ENGINEERING (ACPEE 2020), 2020, : 1457 - 1461
  • [32] Theory of diffusion in a dilute random alloy
    Cameron, LM
    Sholl, CA
    DEFECT AND DIFFUSION FORUM/JOURNAL, 1997, 143 : 143 - 148
  • [33] Random matrix theory for an inter-fragment interaction energy matrix in fragment molecular orbital method
    Yamanaka, Masanori
    CHEM-BIO INFORMATICS JOURNAL, 2018, 18 : 123 - 153
  • [34] BEYOND UNIVERSALITY IN RANDOM MATRIX THEORY
    Edelman, Alan
    Guionnet, A.
    Peche, S.
    ANNALS OF APPLIED PROBABILITY, 2016, 26 (03): : 1659 - 1697
  • [35] Law of addition in random matrix theory
    Zee, A.
    Nuclear Physics, Section B, 474 (03):
  • [36] Action correlations and random matrix theory
    Smilansky, U
    Verdene, B
    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2003, 36 (12): : 3525 - 3549
  • [37] Random matrix theory and the zeros of ζ′(s)
    Mezzadri, F
    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2003, 36 (12): : 2945 - 2962
  • [38] Raney Distributions and Random Matrix Theory
    Forrester, Peter J.
    Liu, Dang-Zheng
    JOURNAL OF STATISTICAL PHYSICS, 2015, 158 (05) : 1051 - 1082
  • [39] Logarithmic universality in random matrix theory
    Splittorff, K
    NUCLEAR PHYSICS B, 1999, 548 (1-3) : 613 - 625
  • [40] Staggered chiral random matrix theory
    Osborn, James C.
    PHYSICAL REVIEW D, 2011, 83 (03):
12345