Small gaps of GOE

2019/01/06 by Renjie Feng, Gang Tian, Feng, Renjie +3 · 2 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Data Management and Algorithms #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1901.01567

arxiv created 2019/01/06 · openalex publication_date 2019/01/06 · arxiv updated 2019/01/08 · openalex created_date 2022/09/03 · openalex updated_date 2026/07/28

Abstract

In this article, we study the smallest gaps of the Gaussian orthogonal ensemble. The main result is that the smallest gaps, after normalized by n, will tend to a Poisson distribution, and the limiting density of the k-th normalized smallest gaps is 2x^2k-1e^-x²/(k-1)!.

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