Mean-field bounds for Poisson-Boolean percolation

Abstract

We establish the mean-field bounds γ ≥ 1, δ ≥ 2 and ≥ 2 on the critical exponents of the Poisson-Boolean continuum percolation model under a moment condition on the radii; these were previously known only in the special case of fixed radii (in the case of γ), or not at all (in the case of δ and ). We deduce these as consequences of the meanfield bound β ≤ 1, recently established under the same moment condition [DRT20], using a relative entropy method introduced by the authors in previous work [DM21].and the critical parameter of the model is