BIRS Workshop Lecture Videos
Beta ensemble at high temperature Dumaz, Laure
In this talk, we will be interested in the behavior of beta (Hermite) ensembles in the microscopic regime. Thanks to the tridiagonal model discovered by Dumitriu and Edelman, Ramirez, Rider and Virag (for the edge) and Valko and Virag (for the bulk) were able to characterize the limiting point processes through a family of coupled diffusions. We use this approach to derive the large temperature limit i.e. the regime where the parameter beta tends to zero. Thanks to a careful analysis of the diffusions, we prove the convergence towards Poissonian point processes (joint works with Romain Allez).
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