Large Deviations in One-Dimensional Random Sequential Adsorption

Abstract

In a random sequential adsorption process, objects are deposited randomly, irreversibly, and sequentially; if an attempt to add an object results in an overlap with previously deposited objects, the attempt is discarded. The process continues until the system reaches a jammed state when no further additions are possible. Exact analyses have been performed only in one-dimensional models, and the average number of absorbed particles has been computed in a few solvable situations. We analyze a process in which landing on an empty site is allowed when at least b neighboring sites on the left and the right are empty. For the minimal model (b = 1), we compute the full counting statistics of the occupation number.