Concentration of the spectral measure for large matrices.
Stability of precise Laplace's method under approximations; Applications
We study the fluctuations around non degenerate attractors of the empirical measure under mean field Gibbs measures. We prove that a mild change of the densities of these measures does not affect the central limit theorems. We apply this result to generalize the assumptions of [3] and [12] on the densities of the Gibbs measures to get precise Laplace estimates.
Lectures on Logarithmic Sobolev Inequalities
Moderate deviations for the spectral measure of certain random matrices
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