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

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

2008-01-27

arxiv.org/abs/0801.4156v1

Mathematics

Probability

30 pages

Scientific paper

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.

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