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Small gaps of GSE

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arxiv 2409.03324 v1 pith:EL7X7D3U submitted 2024-09-05 math.PR

Renjie Feng , Jiaming Li , Dong Yao This is my paper · ORCID
classification math.PR
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abstract

In this paper, we study the smallest gaps for the Gaussian symplectic ensemble (GSE). We prove that the rescaled smallest gaps and their locations converge to a Poisson point process with an explicit rate. The approach provides an alternative proof for the GOE case and complements the results in \cite{FTW}. By combining the main results from \cite{BB, FTW, FW2}, the study of the smallest gaps for the classical random matrix ensembles C$\beta$E and G$\beta$E for $\beta = 1, 2,$ and $4$ is now complete.

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  1. Smallest gaps of the two-dimensional Coulomb gas

    math.PR 2025-07 conditional novelty 7.0 of 10

    For a general potential, the smallest gaps of the 2D Coulomb gas at beta=2 are of order n^{-3/4} and converge to a Poisson point process with intensity determined by the equilibrium density.

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