Some Properties of k-Step Exclusion Processes

We introduce k-step exclusion processes as generalizations of the simple exclusion process. We state their main equilibrium properties when the underlying stochastic matrix corresponds to a random walk or is positive recurrent and reversible. Finally, we prove laws of large numbers for tagged and second-class particles     

Microscopic structure of the k-step¶exclusion process

We review the hydrodynamics and discuss the shock, rarefaction fan and contact discontinuity at a microscopic level for a one-dimensional totally asymmetric k-step exclusion process. In particular we define a microscopical object that identifies the shock in the decreasing case. Received: 9 April 2002