A sharp small deviation inequality for the largest eigenvalue of a random matrix

dvi ps pdf Séminaire de probabilités (2005), volume XXXVIII (LNM 1857).

We prove non-asymptotic bounds on small deviation probabilities for the largest eigenvalue of a complex Hermitian Gaussian random matrix. This can be seen as a quantitative version of Tracy-Widom limit theorem. The same results have been obtained independently by Michel Ledoux using different techniques.

E-mail :
aubrun (arrobas) math. univ-lyon1. fr

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