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BIMSA-Tsinghua Quantum Symmetry Seminar
On joint moments of characteristic polynomials from the CUE
On joint moments of characteristic polynomials from the CUE
Organizers
Speaker
Fei Wei
Time
Friday, January 10, 2025 4:00 PM - 5:00 PM
Venue
A3-3-301
Online
Zoom 242 742 6089
(BIMSA)
Abstract
In this talk, I will firstly introduce some background on the problem of joint moments of the characteristic polynomial of a random unitary matrix. Secondly, I will discuss the connections between joint moments and integrable systems, specifically, connections to solutions of the sigma-Painleve V and the sigma-Painleve III' equations, respectively. Thirdly, I will talk about the applications of these results, including explicit formulae for joint moments of finite matrix size, an efficient way to compute the expectation of some random variables arise from a determinantal process.