EXPONENTIAL WAITING TIME FOR A BIG GAP IN A ONE-DIMENSIONAL ZERO-RANGE PROCESS

The first time that the N sites to the right of the origin become empt y in a one-dimensional zero-range process is shown to converge exponen tially fast, as N --> infinity, to the exponential distribution, when divided by its mean. The initial distribution of the process is assume d to be one of the extremal invariant measures nu(rho), rho is-an-elem ent-of(0, 1), with density rho/(1 - rho). The proof is based on the cl assical Burke theorem.