Salle de conférence Louis Michel
Speaker: Grégory Schehr, LPTMS
Title: Large deviations of the top eigenvalue of random matrices and applications in statistical physics
Abstract: The statistical properties of the largest eigenvalue of a random matrix are of interest in diverse fields such as in the stability of large ecosystems, in disordered systems and related stochastic growth processes, in statistical data analysis and even in string theory. In this talk I will discuss the developments in the theory of extremely rare fluctuations (large deviations) of the largest eigenvalue using a Coulomb gas approach. I will discuss in particular the third-order phase transition which separates the left tail from the right tail, a transition akin to the so-called Gross-Witten-Wadia phase transition found in 2-d lattice quantum chromodynamics.