Matrix representation of the stationary measure for the multispecies TASEP

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.

24 pages, 3 figures

References in corpus (4)

• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics
• Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
• Multiclass processes, dual points and M/M/1 queues

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