Alfredo Deaño

Painlevé equations and non-Hermitian random matrix ensembles

We present recent results on the connection between Painlevé equations and NxN non-Hermitian ensembles of random matrices, in particular those models arising from classical cases with the addition of point charges in the complex plane. The link with Painlevé transcendents can be established both for finite N and as the size of the matrices N tends to infinity, involving different families of solutions in each case. As examples we consider the lemniscate ensemble and truncations of unitary matrices.

This is joint work with Nick Simm (University of Sussex, United Kingdom), and based on the preprint available on https://arxiv.org/abs/1909.06334.