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.

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Cited by in corpus (4)

• Integrability in the weak noise theory
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• High moments of the SHE in the clustering regimes
• Temporal increments of the KPZ equation with general initial data