Discrete-time TASEP with holdback

We study the following interacting particle system. There are ρn particles, ρ<1, moving clockwise (“right”), in discrete time, on n sites arranged a circle. Each site may contain at most one particle. At each move to right-neighbor according rules. If its is occupied by another particle, does not move. has unoccupied (“holes”) as neighbors both sides, it moves right with probability 1. hole and an left-neighbor, 0h, condensation phenomenon occurs, namely formation persistence large clusters; particular, case p(1−ρ)h described theorem.