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
Citation
Sabine Jansen. "Continuum percolation for Gibbsian point processes with attractive interactions." Electron. J. Probab. 21 1 - 22, 2016. https://doi.org/10.1214/16-EJP4175
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