On the large deviations of traces of random matrices

Fanny Augeri

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arXiv · 1605.03894

On the large deviations of traces of random matrices

Fanny Augeri

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Abstract

We present large deviations principles for the moments of the empirical spectral measure of Wigner matrices and empirical measure of $β$-ensembles in three cases : the case of Wigner matrices without Gaussian tails, that is Wigner matrices whose entries have tail distributions decreasing as $e^{-ct^α}$, for some constant $c>0$ and with $α\in (0,2)$, the case of Gaussian Wigner matrices, and the case of $β$-ensembles associated with a convex potential with polynomial growth.

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Fanny Augeri. 2016-05-12. On the large deviations of traces of random matrices. https://arxiv.org/abs/1605.03894

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