Continuum percolation for Gibbsian point processes with attractive interactions

Jansen, Sabine (2016) Continuum percolation for Gibbsian point processes with attractive interactions. Electronic Journal of Probability, 21. p. 47. ISSN 1083-6489

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We study the problem of continuum percolation in infinite volume Gibbs measures for particles with an attractive pair potential, with a focus on low temperatures (large β). The main results are bounds on percolation thresholds ρ ± (β) in terms of the density rather than the chemical potential or activity. In addition, we prove a variational formula for a large deviations rate function for cluster size distributions. This formula establishes a link with the Gibbs variational principle and a form of equivalence of ensembles, and allows us to combine knowledge on finite volume, canonical Gibbs measures with infinite volume, grand-canonical Gibbs measures

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Probability and Statistics Research Group
Subjects: Q Science > QA Mathematics
Depositing User: Richard Chambers
Date Deposited: 13 Jan 2017 15:16
Last Modified: 23 Jan 2018 10:31

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