Our monthly meeting will take place on Monday the 29nd of March, from 4pm to 6pm (Central European Time). Our speakers will be Emma Bailey and Gregory Schehr. The zoom link will be sent to the members of the project through the mailing list. If you are interested in participating and you are not a PIICQ participant, please register sending us an email!
First talk by Emma Bailey at 4pm
Title: Branching random walks, characteristic polynomials, and zeta: log-correlation, moments, and extrema.
Abstract: In this talk I will introduce three log-correlated processes and present results on their moments (and moments of moments), and how these relate to their extremes. This study features connections with integrable systems (in particular Toeplitz and Hankel determinants), RH problems, the Fyodorov-Hiary-Keating conjectures, Painlevé equations, Young diagrams, large deviations and more.
This talk will include work joint with Louis-Pierre Arguin, Theo Assiotis, Jon Keating.
Second talk by Gregory Schehr at 5pm
Title: Exact persistence exponent for the 2d-diffusion equation: from random polynomials to truncated random matrices.
Abstract: After an introduction to persistence probabilities and related first-passage time in statistical physics, I will discuss a specific example: the 2d diffusion equation with random initial conditions. The persistence probability in this problem turns out to be related to the probability of no real root for Kac random polynomials. I will show that this probability can be computed by using yet another connection, namely to the truncated orthogonal ensemble of random matrices.