We establish the mean-field bounds , and 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 mean-field bound , recently established under the same moment condition , using a relative entropy method introduced by the authors in previous work .
The second author was supported by the Australian Research Council (ARC) Discovery Early Career Researcher Award DE200101467. The authors thank Tom Hutchcroft for helpful comments, and also an anonymous referee for valuable and detailed feedback on an earlier version of this paper.
"Mean-field bounds for Poisson-Boolean percolation." Electron. J. Probab. 28 1 - 24, 2023. https://doi.org/10.1214/23-EJP923