2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57181It is now believed that the limiting distribution function of the largest eigenvalue in the three classic random matrix models GOE, GUE and GSE describe new universal limit laws for a wide variety of processes arising in mathematical physics and interacting particle systems. These distribution functions, expressed in terms of a certain Painlevé II function, are described and their occurences surveyed.Mathematical Physics82D30, 60K37text