Poisson statistics at the edge of Gaussian $\beta$-ensemble at high temperature

Abstract : 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 $n\to +\infty$. 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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https://hal.archives-ouvertes.fr/hal-01777520
Submitted on : Wednesday, May 16, 2018 - 11:22:20 AM
Last modification on : Friday, September 20, 2019 - 4:34:03 PM
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• HAL Id : hal-01777520, version 1
• ARXIV : 1804.08214

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Cambyse Pakzad. Poisson statistics at the edge of Gaussian $\beta$-ensemble at high temperature. 2018. ⟨hal-01777520⟩

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