Poisson statistics at the edge of Gaussian beta-ensembles at high temperature

2018/04/23 by Pakzad, Cambyse · 1 citation
#60B20 #60F05 #60G70 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1804.08214

Abstract

We study the asymptotic edge statistics of the Gaussian β-ensemble, a collection of n particles, as the inverse temperature β tends to zero as n tends to infinity. In a certain decay regime of β, the associated extreme point process is proved to converge in distribution to a Poisson point process as n→ +∞. We also extend a well known result on Poisson limit for Gaussian extremes by showing the existence of an edge regime that we did not find in the literature.

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• Large deviations at the edge for 1D gases and tridiagonal random matrices at high temperature

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