Top Eigenvalue of a Random Matrix: Large deviations

by Satya Majumdar (LPTMS Paris)

Friday 13 Dec 2013, 14:00 → 15:00 Europe/Zurich

Auditoire Stueckelberg (Geneva University)

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, in statistical data analysis and even in string theory. In this talk I'll discuss some recent developments in the theory of extremely rare fluctations (large deviations) of the largest eigenvalue using a Coulomb gas method. Such rare fluctuations have also been measured in recent experiments in coupled laser systems. I'll also discuss recent applications of this Coulomb gas method in three different problems: entanglement in a bypartite system, conductance fluctuations thorugh a mesoscopic cavity and the vicious random walkers problem.