Intermittency in random maps

The escape probability for a random walk on a one-dimensional lattice is discussed in terms of random maps. The global dynamics is found to be intermittent: the laminar regions with long sojourn near the upper fixed point are broken by irregular bursts. Intermittency emerges even if the Sinai condition is not satisfied. It is shown that, if P is the probability of choosing the upper map, the average laminar length diverges as (1−P)−α.