Derives all-order large-N asymptotics for the β-ensemble partition function Z_N[V] with Nβ=2P fixed, using loop equations on the thermal equilibrium measure supported on the whole line.
Poisson statistics at the edge of Gaussian beta-ensembles at high temperature
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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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2024 1verdicts
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Asymptotics of the partition function for $\beta$-ensembles at high temperature
Derives all-order large-N asymptotics for the β-ensemble partition function Z_N[V] with Nβ=2P fixed, using loop equations on the thermal equilibrium measure supported on the whole line.