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

Davide Gabrielli

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arXiv · 0801.4156

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

Davide Gabrielli

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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.

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Davide Gabrielli. 2008-01-27. From combinatorics to large deviations for the invariant measures of some multiclass particle systems. https://arxiv.org/abs/0801.4156

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