Heat kernel upper bounds for interacting particle systems

TL;DR

This paper establishes diffusive upper bounds on transition probabilities for a tagged particle in the symmetric simple exclusion process, using spectral gap estimates and Carne-Varopoulos type off-diagonal bounds.

Contribution

It introduces new spectral gap estimates for finite-volume dynamics and derives off-diagonal bounds, advancing understanding of particle system transition probabilities.

Findings

Diffusive upper bounds for tagged particle transition probabilities

Spectral gap estimates for finite-volume dynamics

Off-diagonal Carne-Varopoulos type estimates

Abstract

We show a diffusive upper bound on the transition probability of a tagged particle in the symmetric simple exclusion process. The proof relies on optimal spectral gap estimates for the dynamics in finite volume, which are of independent interest. We also show off-diagonal estimates of Carne-Varopoulos type.