Fluctuations for linear statistics of large random matrices: the case of non-analytic functionals

Orateur: NAJIM Jamal
Localisation: Université de Marne-la-vallée, France
Type: Journée Bézout-Gatech
Site: UPEM
Salle: 4B 08R
Date de début: 18/12/2013 - 11:00
Date de fin: 18/12/2013 - 11:45

Consider two large random matrix models of interest in the applications: the large covariance matrix and the signal plus noise model. In this talk, we will briefly describe the fluctuations of the linear spectral statistics associated to these models. Often in large random matrix theory, the normalized trace of the resolvent is an efficient device to describe the spectrum and its fluctuations. The central part of the talk will be devoted to the presentation of a method which enables to recover the fluctuations for functions with low regularity (say 3 times differentiable functions) from the fluctuations of the trace of the resolvent. We will rely on Helffer-Sjostrand formula to represent the linear statistics of interest and on recent variance estimates obtained by Shcherbina.