From combinatorics to large deviations for the invariant measures of some multiclass particle systems

TL;DR

This paper establishes large deviation principles for invariant measures of multiclass TASEP and HAD processes on a torus, using combinatorial collapsing procedures to analyze their probabilistic behavior.

Contribution

It introduces a combinatorial collapsing framework to derive large deviation principles for multiclass particle systems, extending previous methods to more complex models.

Findings

Large deviation principles proved for invariant measures

Rate functionals expressed via variational problems

Results specifically detailed for 2-class processes

Abstract

We prove large deviation principles (LDP) for the invariant measures of the multiclass totally asymmetric simple exclusion process (TASEP) and the multiclass Hammersely-Aldous-Diaconis (HAD) process on a torus. The proof is based on a combinatorial representation of the measures in terms of a \emph{collapsing procedure} introduced in \cite{A} for the 2-class TASEP and then generalized in \cite{FM1}, \cite{FM2} and \cite{FM3} to the multiclass TASEP and the multiclass HAD process. The rate functionals are written in terms of variational problems that we solve in the cases of 2-class processes.