Abstract: This talk will introduce the notion of Gaussian and almost Gaussian log-correlated fields. These are a class of random (or almost random) functions many of whose statistics are predicted to coincide in a large system-size limit. Examples of these objects include: (1) the logarithm of the Riemann zeta function on the critical line (conjecturally) (2) the log-characteristic polynomial of Haar distributed unitary random matrices (and others), (3) the deviations of Birkhoff sums of substitution dynamical systems (conjecturally) In some cases, this behavior can be proven. This talk will focus on the extreme values of these objects. It will also introduce an approach towards estimating the maximum that works for many distributions of random matrices. This is based on joint works with Gaultier Lambert, Younghwan Son, and Ofer Zeitouni.
Tue, 17/05/2016 - 14:00 to 15:00
Manchester building, Hebrew University of Jerusalem, (Room 209)