Mixing times for the stochastic $p$-Laplace equation

TL;DR

This paper reviews and provides explicit bounds on the mixing times of the stochastic p-Laplace equation with additive noise, highlighting the long-term behavior and asymptotics for p>1.

Contribution

It offers explicit quantitative upper and lower estimates for the mixing times of the stochastic p-Laplace equation, summarizing existing results in a comprehensive table.

Findings

Explicit upper and lower bounds for mixing times

Summary of asymptotic behavior of mixing times

Compilation of existing quantitative results

Abstract

We give an overview on existing quantitative results on long-time behavior of the stochastic $p$-Laplace equation with additive Wiener noise, $p>1$. We summarize the existing results in a table. We give explicit quantitative upper and lower estimates for the $\varepsilon$-mixing times of the stochastic $p$-Laplace equations for $p>1$. We summarize the mixing time asymptotics in a table.