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Duality for Random Sequential Adsorption on a Lattice†

Published online by Cambridge University Press:  12 September 2008

Y. Fan  and
J. K. Percus
Y. Fan
Affiliation:
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012
J. K. Percus
Affiliation:
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012
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Abstract

If particles are dropped randomly on a lattice, with a placement being cancelled if the site in question or a nearest neighbor is already occupied, an ensemble of restricted random walks is created. We seek the time dependence of the expected occupation of a given site. It is shown that this problem reduces to one of enumerating walks from the given site in which a move can only be made to a previously occupied site or one of its nearest neighbors.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 1 , Issue 3 , September 1992 , pp. 219 - 222
Copyright
Copyright © Cambridge University Press 1992

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References

[1]Dickman, R., Wang, J. S. and Jensen, I. (1991) Random Sequential Adsorption: Series and Virial Expansions. J. Chem. Phys. 94, 8252.CrossRefGoogle Scholar
[2]Fan, Y. and Percus, J. K. (1991) Asymptotic Coverage in Random Sequential Adsorption on a Lattice. Phys. Rev. A 44, 5099.CrossRefGoogle ScholarPubMed
[3]Tarjus, G., Schaaf, P. and Talbot, J. (1991) Random Sequential Addition: A Distribution Function Approach. J. Stat. Phys. 63, 167.CrossRefGoogle Scholar