Modified Macdonald polynomials and the multispecies zero range process: II

In a previous part of this work, we gave a new tableau formula for the modified Macdonald polynomials H lambda(X;q,t), using a weight on tableaux involving the queue inversion(quinv)statistic. In this paper we explicitly describe a connection between these combinatorial objectsand a class of multispecies totally asymmetric zero range processes (mTAZRP) on a ring, with site-dependent jump-rates. We construct a Markov chain on the space of tableaux ofa given shape, which projects to the mTAZRP, and whose stationary distribution can be expressed in terms of quinv-weighted tableaux. We deduce that the mTAZRP has a partition function given by the modified Macdonald polynomial H lambda(X;1,t). The novelty here in comparison to previous works relating the stationary distribution of integrable systems to symmetric functions is that the variablesx1,...,xnare explicitly present as hopping rates in the mTAZRP. We also obtain interesting symmetry properties of the mTAZRP probabilitie sunder permutation of the jump-rates between the sites. Finally, we explore a number of interesting special cases of the mTAZRP, and give explicit formulas for particle densities and correlations of the process purely in terms of modified Macdonald polynomials