Cluster size distributions in particle systems with asymmetric dynamics - art. no. 056114

We present exact and asymptotic results for clusters in the one-dimensional totally asymmetric exclusion process (TASEP) with two different dynamics. The expected length of the largest cluster is shown to diverge logarithmica lly with an increasing system size for ordinary TASEP dynamics and as a log arithm divided by a double logarithm for generalized dynamics, where the ho pping probability of a particle depends on the size of the cluster it belon gs to. The connection with the asymptotic theory of extreme order statistic s is discussed in detail. We also consider a related model of interface gro wth, where the deposited particles are allowed to relax to the local gravit ational minimum.