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±(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.Comment: 22 pages. Corrected a statement on lattice gases, added referenc