Stationary measures for the Porous Medium Model

TL;DR

This paper investigates the stationary measures of a one-dimensional kinetically constrained exclusion process, revealing their decomposition into frozen states and mixtures of product measures, advancing understanding of such models.

Contribution

It characterizes the structure of stationary measures for a class of porous medium models with kinetic constraints in one dimension.

Findings

Stationary measures decompose into frozen parts and mixtures of product measures.

Invariant sets can exist with zero probability under these measures.

Provides a detailed description of stationary measures for the model.

Abstract

We study the stationary measures for variants of the Porous Medium Model in dimension 1. These are exclusion processes that belong to the class of kinetically constrained models, in which an exchange can occur between $x$ and $x+1$ only if there is a particle either at $x-1$ or $x+2$. We show that any stationary probability measure can be decomposed into a frozen part and a mixture of product measures (although there exist invariant sets which have zero probability under these measures).