Extreme value problems in random matrix theory and other disordered systems

Abstract

We review some applications of central limit theorems and extreme values statistics in thecontext of disordered systems. We discuss several problems, in particular concerningrandom matrix theory and the generalization of the Tracy–Widom distribution when thedisorder has ‘fat tails’. We underline the relevance of power-law tails for directed polymersand mean-field spin glasses and we point out various open problems and conjectures onthese matters. We find that, in many instances, the assumption of Gaussian disordercannot be taken for granted.