Matrix product solution to an inhomogeneous multi-species TASEP

Chikashi Arita (1) , Kirone Mallick (1)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681

We study a multi-species exclusion process with inhomogeneous hopping rates and find a matrix product representation for the stationary state of this model. The matrices belong to the tensor algebra of the fundamental quadratic algebra associated with the exclusion process. We show that our matrix product representation is equivalent to a graphical construction proposed by Ayyer and Linusson (2012 arXiv:1206.0316), which generalizes an earlier probabilistic construction due to Ferrari and Martin (2007 Ann. Prob. 35 807).

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

Chikashi Arita, Kirone Mallick. Matrix product solution to an inhomogeneous multi-species TASEP. Journal of Physics A: Mathematical and Theoretical, 2013, 46 (8), pp.085002. ⟨10.1088/1751-8113/46/8/085002⟩. ⟨cea-02923903⟩