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

2008/01/27 by Davide Gabrielli, Gabrielli, Davide
Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.0801.4156

openalex publication_date 2008/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 collapsing procedure introduced in \citeA for the 2-class TASEP and then generalized in \citeFM1, \citeFM2 and \citeFM3 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.

Citations

• Multiclass processes, dual points and M/M/1 queues

Related

• Large deviation principle for the stationary measures of open asymmetric simple exclusion processes
• Static large deviations of boundary driven exclusion processes
• The Stationary Measure of a 2-type Totally Asymmetric Exclusion Process
• The Semi-Infinite Asymmetric Exclusion Process: Large Deviations via Matrix Products
• Exceedingly Large Deviations of the Totally Asymmetric Exclusion Process