Processus de saut avec interaction selon les plus proches particules. (Jump processes with nearest neighbour particle interaction) (Q1090015)

The author considers a class of infinite particle systems on \({\mathbb{Z}}\) where the number of particles is conserved and each particle can only jump to the empty sites between its left and right nearest neighbour according to a law which only depends on the distances to its right and left neighbour. A condition is given that ensures the existence of reversible states. When this condition is satisfied, the reversible states form a one- parameter family of renewal measures and the author proves (under mild conditions on the jump law) that every translation invariant stationary state for this evolution is a convex combination of these renewal measures.