  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.
