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arXiv · 2007.06505

Lyapunov exponents of the SHE for general initial data

Promit Ghosal·Yier Lin
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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.

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BibTeXRIS

Promit Ghosal, Yier Lin. 2020-07-13. Lyapunov exponents of the SHE for general initial data. https://doi.org/10.1214/22-aihp1253

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