Abstract
We establish a large deviation principle for the spectral measure of a large class of discrete Coulomb gas. The setting includes invariant ensembles from the classical orthogonal polynomials which are the discrete analogues of the continuous random matrix models. The proof requires a refinement of the arguments used in the continuous framework due to the constraint that may appear in the description of the rate functional. Our analysis closely follows the investigations of K. Johansson at the level of the largest eigenvalue, that is recovered here by a change of variables.
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Féral, D. (2008). On large deviations for the spectral measure of discrete Coulomb gas. In: Donati-Martin, C., Émery, M., Rouault, A., Stricker, C. (eds) Séminaire de Probabilités XLI. Lecture Notes in Mathematics, vol 1934. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77913-1_2
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DOI: https://doi.org/10.1007/978-3-540-77913-1_2
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