Seminar

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In random matrix theory, evaluating the probability that spectral quantities, such as the empirical measure and the largest eigenvalue takes unusual values (or more technically: proving a large deviation principle) is a difficult question. Indeed, whereas it has been successfully investigated in the case of the GOE/GUE as well as in some other particulars cases (such as matrices with entries with tails heavier than Gaussian), it remains mysterious in a more general setting, for which one generally only has concentration bounds. However, there has been important advances on this question through the use of spherical integrals (also known as Harish Chandra-Itzykson-Zuber integrals) as proxy for the largest eigenvalues. In this talk I will explain how the asymptotics of these spherical integrals behave and how to use them to obtain the large deviations of the largest eigenvalues for several sub-Gaussian random matrix models. This talk is based on several joint works with Alice Guionnet and with Fanny Augeri.

Spherical Integrals And Large Deviations Of The Largest Eigenvalues For Sub-Gaussian Random Matrices