Supercritical sharpness for Voronoi percolation

• 成果类型: Article
• 署名作者: Dembin, Barbara; Severo, Franco
• 署名单位: Universites de Strasbourg Etablissements Associes; Centre National de la Recherche Scientifique (CNRS); Universite de Strasbourg; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Jean Monnet; Universite Lyon 1; Ecole Centrale de Lyon; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051; 1432-2064
• DOI: 10.1007/s00440-024-01351-8
• 发表日期: 2026-06
• 页码: 31-72
• 关键词: Voronoi percolation; Supercritical sharpness; RENORMALIZATION; quenched invariance-principles; critical probability; chemical distance; PHASE-TRANSITION; large deviations; critical-points; random-walks; homogenization; REGULARITY

摘要

We prove that the supercritical phase of Voronoi percolation on R-d, d >= 3, is well behaved in the sense that for every p>p(c)(d) local uniqueness of macroscopic clusters happens with high probability. As a consequence, truncated connection probabilities decay exponentially fast and percolation happens on sufficiently thick 2D slabs. This is the analogue of the celebrated result of Grimmett and Marstrand for Bernoulli percolation and serves as the starting point for renormalization techniques used to study several fine properties of the supercritical phase.