Large Deviations in Random Sequential Adsorption

P. L. Krapivsky

Published 2020-09-18Version 1

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.