Small gaps of GSE

TL;DR

This paper investigates the smallest gaps in the Gaussian symplectic ensemble (GSE), proving their convergence to a Poisson process and completing the understanding of smallest gaps across classical random matrix ensembles.

Contribution

It provides an alternative proof for the GSE case and completes the analysis of smallest gaps for CβE and GβE ensembles for β=1,2,4.

Findings

Smallest gaps in GSE converge to a Poisson point process.

The approach offers an alternative proof for the GOE case.

The study completes the analysis of smallest gaps for classical ensembles.

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.