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Résumé de communication

Résumé 295 :

Concentration inequalities for random matrices
Ledoux, Michel
Université de Toulouse

Exponential tail inequalities are a central theme in probability and statistics, with a huge range of applications to both asymptotic statements and more quantitative controls. In particular, measure concentration ideas and methods have proved very powerful in the recent years to reach exponential bounds for functionals far beyond the traditional sums of independent random variables, with applications in statistics, geometric and combinatorial probability theory and functional analysis. The study of random matrix and random growth models raised recently a number of issues on non-asymptotic bounds. In particular, exponential inequalities in the large deviations or central limit theorem regimes for spectral measures of random matrices, or in the fluctuation regime of their extremal eigenvalues towards the Tracy-Widom distribution, require new adapted and specific tools and methods. We present some results and approaches developed recently towards this goal in the context of families of covariance matrices of potential use in statistical applications.