English

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

Probability 2008-01-29 v1

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.

Keywords

Cite

@article{arxiv.0801.4156,
  title  = {From combinatorics to large deviations for the invariant measures of some multiclass particle systems},
  author = {Davide Gabrielli},
  journal= {arXiv preprint arXiv:0801.4156},
  year   = {2008}
}

Comments

30 pages

R2 v1 2026-06-21T10:06:53.963Z