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Milind Hegde: Understanding the upper tail behaviour of the KPZ equation via the tangent method

Time: Tue 2022-10-04 15.15 - 16.15

Location: Zoom

Video link: Meeting ID: 698 3346 0369

Lecturer: Milind Hegde (Columbia University)

Abstract

The Kardar-Parisi-Zhang (KPZ) equation is a canonical non-linear stochastic PDE believed to describe the evolution of a large number of planar stochastic growth models which make up the KPZ universality class. A particularly important observable is the one-point distribution of its analogue of the fundamental solution, which has featured in much of its recent study. However, in spite of significant recent progress relying on explicit formulas, a sharp understanding of its upper tail behaviour has remained out of reach. In this talk we will discuss a geometric approach, related to the tangent method introduced by Colomo-Sportiello and rigorously implemented by Aggarwal for the six-vertex model. The approach utilizes a Gibbs resampling property of the KPZ equation and yields a sharp understanding for a large class of initial data.