Poisson statistics at the edge of Gaussian β-ensemble at high temperature

We study the asymptotic edge statistics of the Gaussian beta-ensemble, a collection of n particles, as the inverse temperature beta tends to zero as n tends to infinity. In a certain decay regime of beta, the associated extreme point process is proved to converge in distribution to a Poisson point process as n -> +infinity. 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.