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Pré-Publication, Document De Travail Année : 2023

CLT for Beta ensembles at high-temperature, and for integrable systems: a transfer operator approach

Résumé

In this paper, we prove a polynomial Central Limit Theorem for several integrable models, and for the $\beta$ ensembles at high-temperatures with polynomial potential. Furthermore, we are able to relate the mean values, the variances and the correlations of the moments of these integrable systems with the one of the $\beta$ ensembles. Moreover, we show that for several integrable models, the local functions' space-correlations decay exponentially fast.
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Dates et versions

hal-04096307 , version 1 (12-05-2023)

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Guido Mazzuca, Ronan Memin. CLT for Beta ensembles at high-temperature, and for integrable systems: a transfer operator approach. 2023. ⟨hal-04096307⟩
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