香蕉视频

Title:聽KPZ universality: last passage percolation, polymers and particles.

Abstract:聽KPZ universality describes a scaling behaviour that differs from the central limit theorem by the size of the fluctuations ($n^{1/3}$ instead of $n^{1/2}$) and the limiting distribution. Instead of the Gaussian, the Tracy-Widom distributions from random matrix theory appear in the limit. It is a long standing conjecture that the KPZ universality class contains a large group of models, including particle systems, last-passage and polymer models. Beyond its physical motivation, the study of KPZ universality involves a surprising range of mathematical tools, including algebra, combinatorics, analysis and stochastic calculus. In this talk, I will give an overview of the KPZ universality class and discuss some specific models, based on joint work with Duncan Dauvergne, Nicos Georgiou, Neil O'Connell, Jeremy Quastel, Daniel Remenik and B谩lint Vir谩g.