Critical asymptotic behavior for the Korteweg-de Vries equation and in random matrix theory

Abstract

We discuss universality in random matrix theory and in the study of Hamiltonian partial differential equations. We focus on universality of critical behavior and we compare results in unitary random matrix ensembles with their counterparts for the Korteweg-de Vries equation, emphasizing the similarities between both subjects.Comment: review paper, 19 pages, to appear in the proceedings of the MSRI semester on `Random matrices, interacting particle systems and integrable systems