Processes with a Local Deterministic Interaction: Invariant Bernoulli Measures

TL;DR

This paper introduces a broad class of Markov processes with local interactions, including exclusion and Kawasaki processes, and identifies Bernoulli measures that remain invariant under these dynamics.

Contribution

It generalizes existing models by defining a new class of processes with local deterministic interactions and finds their Bernoulli invariant measures.

Findings

Bernoulli measures are invariant for the new class of processes

Includes exclusion and Kawasaki processes as special cases

Provides a unified framework for local interaction processes

Abstract

A general class of Markov processes with a local interaction is introduced, which includes exclusion and Kawasaki processes as a very particular case. Bernoulli invariant measures are found for this class of processes.