# Top Eigenvalue of a Random Matrix: A tale of tails

**Dr. Satya Majumdar **

CNRS Paris

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 fluctuations (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 bipartite system, conductance fluctuation through a mesoscopic cavity and the vicious random walkers problem.