Matrix representation of the stationary measure for the multispecies TASEP

Martin R. Evans (1, 2) , Pablo A. Ferrari (3) , Kirone Mallick (4)

1 SUPA School of Physics and Astronomy [Edinburgh]
2 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
3 Instituto de matemática e estatística da Universidade de São Paulo
4 IPHT - Institut de Physique Théorique - UMR CNRS 3681

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.

Mots clés: Totally asymmetric simple exclusion process; multi-species systems; Stationary states; matrix representation

Domaines: Probabilités [math.PR]; Mécanique statistique [cond-mat.stat-mech]; Physique mathématique [math-ph]

Martin R. Evans, Pablo A. Ferrari, Kirone Mallick. Matrix representation of the stationary measure for the multispecies TASEP. Journal of Statistical Physics, 2009, 135 (2), pp.217-239. ⟨10.1007/s10955-009-9696-2⟩. ⟨cea-02924963⟩