The Annals of Applied Probability

Exact and approximate results for deposition and annihilation processes on graphs

Mathew D. Penrose and Aidan Sudbury

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We consider random sequential adsorption processes where the initially empty sites of a graph are irreversibly occupied, in random order, either by monomers which block neighboring sites, or by dimers. We also consider a process where initially occupied sites annihilate their neighbors at random times.

We verify that these processes are well defined on infinite graphs, and derive forward equations governing joint vacancy/occupation probabilities. Using these, we derive exact formulae for occupation probabilities and pair correlations in Bethe lattices. For the blocking and annihilation processes we also prove positive correlations between sites an even distance apart, and for blocking we derive rigorous lower bounds for the site occupation probability in lattices, including a lower bound of 1/3 for Z2. We also give normal approximation results for the number of occupied sites in a large finite graph.

Article information

Ann. Appl. Probab., Volume 15, Number 1B (2005), 853-889.

First available in Project Euclid: 1 February 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 05C05: Trees 60C05: Combinatorial probability 60F05: Central limit and other weak theorems

Random sequential adsorption interacting particle systems trees central limit theorems


Penrose, Mathew D.; Sudbury, Aidan. Exact and approximate results for deposition and annihilation processes on graphs. Ann. Appl. Probab. 15 (2005), no. 1B, 853--889. doi:10.1214/105051604000000765.

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