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Painlevé equations and non-Hermitian random matrix ensembles

Presented by: 
Alfredo Deaño University of Kent
Monday 9th September 2019 - 16:00 to 17:00
INI Seminar Room 1
In this talk 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 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).
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons