Matrix Representation of the Stationary Measure for the Multispecies TASEP

Martin R. Evans, Pablo A. Ferrari, Kirone Mallick

Research output: Contribution to journalArticlepeer-review

Abstract

In this work we construct the stationary measure of the N species totally asymmetric simple exclusion process in a matrix product formulation. We make the connection between the matrix product formulation and the queueing theory picture of Ferrari and Martin. In particular, in the standard representation, the matrices act on the space of queue lengths. For N > 2 the matrices in fact become tensor products of elements of quadratic algebras. This enables us to give a purely algebraic proof of the stationary measure which we present for N=3.

Original languageEnglish
Pages (from-to)217-239
Number of pages23
JournalJournal of Statistical Physics
Volume135
Issue number2
DOIs
Publication statusPublished - Apr 2009

Keywords

  • Totally asymmetric simple exclusion process
  • Multi-species systems
  • Stationary states
  • Matrix representation
  • SIMPLE EXCLUSION PROCESS
  • MODEL
  • PARTICLES

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