Year: 2026
Type: article
Abstract: We consider Poisson Boolean percolation on Rd with power-law distribution on the radius with a finite d-moment for d≥2. We prove that subcritical sharpness occurs for all but a countable number of power-law distributions. This extends the results of Duminil-Copin–Raoufi–Tassion (Ann. Henri Lebesgue 3 (2020) 677–700) where subcritical sharpness is proved under the assumption that the radii distribution has a 5d−3 finite moment. Our proofs techniques are different from (Ann. Henri Lebesgue 3 (2020) 677–700): we do not use a randomized algorithm and rely on specific independence properties of Boolean percolation, inherited from the underlying Poisson process. We also prove supercritical sharpness for any distribution with a finite d-moment and the continuity of the critical parameter for the truncated distribution when the truncation goes to infinity.
Source: The Annals of Probability
DOI: 10.1214/25-aop1771
Authors: Barbara Dembin, Vincent Tassion
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: European Commission
OpenAlex ID: W4294789860