Small gaps of GSE

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${\hat{I}}^2$E and G${\hat{I}}^2$E for ${\hat{I}}^2=1,2,$ and $4$ is now complete.