Abstract
We prove large deviation principles for the distribution of the empirical measure of the eigenvalues of Lax matrices following the Generalized Gibbs ensembles of the classical Toda chain introduced in [9]. We deduce the almost sure convergence of this empirical measure towards a limit which we describe in terms of the limiting empirical measure of Beta-ensembles. Our results apply to general smooth potentials.
Funding Statement
This project has received funding from the European Research Council (ERC) under the European Union Horizon 2020 research and innovation program (grant agreement No. 884584).
Citation
Alice Guionnet. Ronan Memin. "Large deviations for Gibbs ensembles of the classical Toda chain." Electron. J. Probab. 27 1 - 29, 2022. https://doi.org/10.1214/22-EJP771
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