16/03/2022, 16:00 — 17:00 — Sala P3.10, Pavilhão de Matemática Online
Guillaume Barraquand, ENS Paris
Invariant measures for the KPZ equation
It has been known for a long time that the Brownian motion is an invariant measure for the Kardar-Parisi-Zhang equation on the real line. For KPZ growth on bounded domains, however, the situation is more complicated. Stationary measures are typically not invariant by translation, non Gaussian, and they depend non trivially on boundary conditions. I will review recent progress on the characterization of invariant measures for the KPZ equation on a segment $[0,L]$ and on the half-line $\mathbb{R}_+$. Based on joint works with Pierre Le Doussal and Ivan Corwin.
