LARGE DEVIATIONS FOR GENERALIZED GIBBS ENSEMBLES OF THE CLASSICAL TODA CHAIN

Alice Guionnet (1, 2, 3) , Ronan Memin (1, 2, 3)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 ENS de Lyon - École normale supérieure de Lyon
3 CNRS - Centre National de la Recherche Scientifique

We derive large deviations principles for the distribution of the empirical measure of the equilibrium measure for the Generalized Gibbs ensembles of the classical Toda chain introduced in [11]. We deduce its almost sure convergence and characterize its limit in terms of the limiting measure of Beta-ensembles. Our results apply to general smooth potentials.

Domaines: Mathématiques [math]; Probabilités [math.PR]

Alice Guionnet, Ronan Memin. LARGE DEVIATIONS FOR GENERALIZED GIBBS ENSEMBLES OF THE CLASSICAL TODA CHAIN. 2021. ⟨hal-03133224v1⟩