Open Access
2023 Mean-field bounds for Poisson-Boolean percolation
Vivek Dewan, Stephen Muirhead
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Electron. J. Probab. 28: 1-24 (2023). DOI: 10.1214/23-EJP923


We establish the mean-field bounds γ1, δ2 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 mean-field bound β1, recently established under the same moment condition [8], using a relative entropy method introduced by the authors in previous work [7].


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.


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Vivek Dewan. Stephen Muirhead. "Mean-field bounds for Poisson-Boolean percolation." Electron. J. Probab. 28 1 - 24, 2023.


Received: 1 December 2021; Accepted: 14 February 2023; Published: 2023
First available in Project Euclid: 22 February 2023

MathSciNet: MR4551565
zbMATH: 07707089
Digital Object Identifier: 10.1214/23-EJP923

Primary: 60G60
Secondary: 60F99

Keywords: continuum percolation , Critical exponents , mean-field bounds , Poisson-Boolean model

Vol.28 • 2023
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