Roger Van Peski: New limits in (p-adic) integer random matrix theory.

Abstract.

Random matrices over the integers and p-adic integers have been studied since the late 1980s as natural models for random groups appearing in number theory and combinatorics. Recently it has also become clear that the theory has close structural parallels with singular values of complex random matrices, bringing new techniques from integrable probability and motivating new questions. I will outline this area (no background in p-adic matrices will be assumed), discuss exact results and their parallels with classical random matrix theory, and give probabilistic results for products of random matrices. The latter yield interesting new local limit objects analogous to the extended sine and Airy processes in classical random matrix theory.