Lyapunov exponents of the SHE for general initial data
Probability
2023-05-26 v2 Mathematical Physics
math.MP
Abstract
We consider the -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.
Cite
@article{arxiv.2007.06505,
title = {Lyapunov exponents of the SHE for general initial data},
author = {Promit Ghosal and Yier Lin},
journal= {arXiv preprint arXiv:2007.06505},
year = {2023}
}