Title: “Monotonicity of the logarithmic energy for random matrices”.

Abstract: In this talk I will present an entropy functional for the mean empirical spectral distribution of random matrices which appears to be monotonic along the classical limit theorems of Wigner, Tao−Vu and Marčenko−Pastur. I will first give some motivation by recalling known monotonicities of entropy such as Shannon’s entropy along the central limit theorem or Boltzmann’s H-theorem of thermodynamics. Based on joint work with D. Chafaï and P. Youssef.