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arXiv · 2409.03324

Small gaps of GSE

Renjie Feng·Jiaming Li·Dong Yao
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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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Renjie Feng, Jiaming Li, Dong Yao. 2024-09-05. Small gaps of GSE. https://arxiv.org/abs/2409.03324

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