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 FTW. By combining the main results from BB, FTW, FW2, the study of the smallest gaps for the classical random matrix ensembles CβE and GβE for β = 1, 2, and 4 is now complete.
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