Electronic Journal of Probability

Continuum percolation for Gibbsian point processes with attractive interactions

Sabine Jansen

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1469720442

Digital Object Identifier
doi:10.1214/16-EJP4175

Mathematical Reviews number (MathSciNet)
MR3539641

Zentralblatt MATH identifier
1385.60059

Subjects
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]

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

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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