## The Annals of Applied Probability

### Exact and approximate results for deposition and annihilation processes on graphs

#### Abstract

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

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

Dates
First available in Project Euclid: 1 February 2005

https://projecteuclid.org/euclid.aoap/1107271670

Digital Object Identifier
doi:10.1214/105051604000000765

Mathematical Reviews number (MathSciNet)
MR2114992

Zentralblatt MATH identifier
1073.60097

#### Citation

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. https://projecteuclid.org/euclid.aoap/1107271670

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