Inhomogeneous discrete-time exclusion processes

We study discrete time Markov processes with periodic or open boundary conditions and with inhomogeneous rates in the bulk. The Markov matrices are given by the inhomogeneous transfer matrices introduced previously to prove the integrability of quantum spin chains. We show that these processes have a simple graphical interpretation and correspond to a sequential update. We compute their stationary state using a matrix ansatz and express their normalization factors as Schur polynomials. A connection between Bethe roots and Lee-Yang zeros is also pointed out.