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Matrix Representation of the Stationary Measure for the Multispecies TASEP

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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.

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Authors and Affiliations

  1. SUPA, School of Physics, University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JZ, UK

    Martin R. Evans

  2. Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud, Bat 100, 91405, Orsay Cedex, France

    Martin R. Evans

  3. Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, 05311-970, São Paulo, Brasil

    Pablo A. Ferrari

  4. Institut de Physique Théorique, CEA Saclay, 91191, Gif-sur-Yvette Cedex, France

    Kirone Mallick

Authors
  1. Martin R. Evans
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  2. Pablo A. Ferrari
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  3. Kirone Mallick
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Correspondence to Pablo A. Ferrari.

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Evans, M.R., Ferrari, P.A. & Mallick, K. Matrix Representation of the Stationary Measure for the Multispecies TASEP. J Stat Phys 135, 217–239 (2009). https://doi.org/10.1007/s10955-009-9696-2

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  • DOI: https://doi.org/10.1007/s10955-009-9696-2

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