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arXiv · 1208.1223

Continuum percolation for Gibbsian point processes with attractive interactions

Sabine Jansen
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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 $β$). The main results are bounds on percolation thresholds $ρ_\pm(β)$ 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.

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Sabine Jansen. 2012-08-30. Continuum percolation for Gibbsian point processes with attractive interactions. https://arxiv.org/abs/1208.1223

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