Density and Correlation in a Random Sequential Adsorption Model
Charles S. do Amaral, Diogo C. dos Santos
2023, v.29, Issue 5, 695-707
ABSTRACT
We consider the random sequential adsorption process on the one-
dimensional lattice with nearest-neighbor exclusion. In this model, each site
s 2 Z starts empty and a particle will be deposited in it at time ts, where
(ts)s2Z is a sequence of independent random variables uniformly distributed on
the interval [0; 1]. The site will be occupied if both of its neighbors are vacant.
Analytical expressions for the density of occupied sites and the pair correlation
function, for all time t, are well-established and have been obtained through
methods such as generating functions and di erential equations. In this study,
we present a method based on probabilistic arguments for the calculation of
these expressions.
doi:10.61102/1024-2953-mprf.2023.29.5.005
Keywords: Random sequential adsorption; Interacting particles system; Nearest- neighbor
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