# Poisson statistics for matrix ensembles at large temperature

Abstract : In this article, we consider $\beta$-ensembles, i.e. collections of particles with random positions on the real line having joint distribution $\frac{1}{Z_N(\beta)}|\Delta(\lambda)|^\beta e^{- \frac{N\beta}{4}\sum_{i=1}^N\lambda_i^2}d \lambda,$ in the regime where $\beta\to 0$ as $N\to\infty$. We briefly describe the global regime and then consider the local regime. In the case where $N\beta$ stays bounded, we prove that the local eigenvalue statistics, in the vicinity of any real number, are asymptotically to those of a Poisson point process. In the case where $N\beta\to\infty$, we prove a partial result in this direction.
Type de document :
Article dans une revue
Journal of Statistical Physics, Springer Verlag, 2015, 161 (3), pp.633-656. 〈10.1007/s10955-015-1340-8〉
Domaine :

https://hal.archives-ouvertes.fr/hal-01163065
Contributeur : Florent Benaych-Georges <>
Soumis le : vendredi 12 juin 2015 - 07:06:58
Dernière modification le : jeudi 11 janvier 2018 - 06:19:45

### Citation

Florent Benaych-Georges, Sandrine Péché. Poisson statistics for matrix ensembles at large temperature. Journal of Statistical Physics, Springer Verlag, 2015, 161 (3), pp.633-656. 〈10.1007/s10955-015-1340-8〉. 〈hal-01163065〉

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