We introduce and study a natural multispecies variant of the inhomogeneous PushTASEP with site-dependent rates on the finite ring. We show that the stationary distribution of this process is proportional to the ASEP polynomials at q = 1 and t = 0. We do so by constructing a multiline process which projects to the multispecies PushTASEP, and identifying its stationary distribution using time-reversal arguments.
We also study symmetry properties of the process under interchange of the rates associated to the sites out of equilibrium. Lastly, we give explicit formulas for nearest-neighbour two-point correlations in terms of Schur functions. This is joint work with James Martin (arXiv:2310.09740). Work on a generalized model we call the inhomogeneous multispecies t-PushTASEP will be presented by Lauren Williams.
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