Seminar Event Detail

Integrable Systems and Random Matrix Theory

Date:  Monday, March 28, 2022
Location:  ZOOM ID: 926 6491 9790 Virtual (4:00 PM to 5:00 PM)

Title:  Secular coefficients of random unitary matrices

Abstract:   I will discuss the coefficients of the characteristic polynomial of a random unitary matrix. These are commonly known as secular coefficients, and their study was initiated by Diaconis and Gamburd in 2004 who showed that their moments are linked to the combinatorics of magic squares. I will discuss generalisations of this result and some new connections to random permutations and to Gaussian multiplicative chaos theory. This enables us to write down limit theorems for the coefficients in certain circumstances and to partially resolve an open problem of Diaconis and Gamburd who asked about this limit behaviour. This is joint work with Joseph Najnudel (Université Côte d'Azur) and Elliot Paquette (McGill University).

A recording of the talk can be found here.


Speaker:  Nicholas Simm
Institution:  University of Sussex

Event Organizer:   Ahmad Barhoumi


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