Supercritical sharpness for Voronoi percolation

• 成果类型: Article; Early Access
• 署名作者: Dembin, Barbara; Severo, Franco
• 署名单位: Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-024-01351-8
• 发表日期: 2025
• 关键词: 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.