Lyapunov exponents of the SHE for general initial data

Abstract: We consider the 1+1 dimensional stochastic heat equation (SHE) with multiplicative white noise and the Cole-Hopf solution of the Kardar-Parisi-Zhang (KPZ) equation. We show an exact way of computing the Lyapunov exponents of the SHE for a large class of initial data which includes any bounded deterministic positive initial data and the stationary initial data. As a consequence, we derive exact formulas for the upper tail large deviation rate functions of the KPZ equation for general initial data. Joint work with Promit Ghosal.

mathematical physicscombinatoricsprobabilityrepresentation theorystatistics theory

Audience: researchers in the topic

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Junior Integrable Probability Seminar

Series comments: The Junior Integrable Probability Seminar is a series of talks taking place online and involving young researchers working in Integrable Probability and related fields. Go to sites.google.com/view/junior-ips for zoom link and password for the talk a day before the seminar.