Electronic Journal of Probability

Continuum percolation for Gibbsian point processes with attractive interactions

Sabine Jansen

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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 $\beta $). The main results are bounds on percolation thresholds $\rho _\pm (\beta )$ 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

Article information

Electron. J. Probab., Volume 21 (2016), paper no. 47, 22 pp.

Received: 9 March 2015
Accepted: 25 February 2016
First available in Project Euclid: 28 July 2016

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Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C43: Time-dependent percolation [See also 60K35]

continuum percolation stochastic geometry point processes large deviations Gibbs measures Gibbs variational principle

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Jansen, Sabine. Continuum percolation for Gibbsian point processes with attractive interactions. Electron. J. Probab. 21 (2016), paper no. 47, 22 pp. doi:10.1214/16-EJP4175. https://projecteuclid.org/euclid.ejp/1469720442

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