Large deviations in one-dimensional random sequential adsorption
Abstract
In random sequential adsorption (RSA), objects are deposited randomly, irreversibly, and sequentially; attempts leading to an overlap with previously deposited objects are discarded. The process continues until the system reaches a jammed state when no further additions are possible. We analyze a class of lattice RSA models in which landing on an empty site in a segment is allowed when at least b neighboring sites on the left and the right are unoccupied. For the minimal model (b =1 ), we compute the full counting statistics of the occupation number. We reduce the determination of the full counting statistics to a Riccati equation that appears analytically solvable only when b =1 . We develop a perturbation procedure which, in principle, allows one to determine cumulants consecutively, and we compute the variance of the occupation number for all b .
- Publication:
-
Physical Review E
- Pub Date:
- December 2020
- DOI:
- 10.1103/PhysRevE.102.062108
- arXiv:
- arXiv:2009.08609
- Bibcode:
- 2020PhRvE.102f2108K
- Keywords:
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- Condensed Matter - Statistical Mechanics;
- Mathematics - Probability
- E-Print:
- 11 pages, 2 figures