Electronic Journal of Probability
- Electron. J. Probab.
- Volume 21 (2016), paper no. 47, 22 pp.
Continuum percolation for Gibbsian point processes with attractive interactions
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
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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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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