圆形β系综的小间隙

IF 2.1 1区数学 Q1 STATISTICS & PROBABILITY

Annals of Probability Pub Date : 2021-03-01 DOI:10.1214/20-AOP1468

Renjie Feng, Dongyi Wei

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引用次数: 7

摘要

nβ+2β+1，将在分布上收敛为具有某种显式强度的泊松点过程。因此，可以导出第k个最小间隙的极限密度，它与xk（β+1）−1e−xβ+1成比例。特别地，该结果适用于随机矩阵理论中的经典COE、CUE和CSE。证明的重要部分是导出关于塞尔伯格积分的几个恒等式和不等式，它们应该有自己的兴趣。

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Small gaps of circular β-ensemble

n β+2 β+1 , will converge in distribution to a Poisson point process with some explicit intensity. And thus one can derive the limiting density of the k-th smallest gap, which is proportional to xk(β+1)−1e−x β+1 . In particular, the results apply to the classical COE, CUE and CSE in random matrix theory. The essential part of the proof is to derive several identities and inequalities regarding the Selberg integral, which should have their own interest.

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来源期刊

Annals of Probability 数学-统计学与概率论

CiteScore

4.60

自引率

8.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Annals of Probability publishes research papers in modern probability theory, its relations to other areas of mathematics, and its applications in the physical and biological sciences. Emphasis is on importance, interest, and originality – formal novelty and correctness are not sufficient for publication. The Annals will also publish authoritative review papers and surveys of areas in vigorous development.