Russo's Formula, Uniqueness of the Infinite Cluster, and Continuous Differentiability of Free Energy for Continuum Percolation

DOI10.1239/jap/1316796901zbMath1244.60094OpenAlexW2014767400MaRDI QIDQ3094679

Tian-de Guo, Sanguo Zhang, Jian-Ping Jiang

Publication date: 25 October 2011

Published in: Journal of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1239/jap/1316796901

zbMATH Keywords

connectivity functioncontinuum percolationRusso's formulauniqueness of the infinite cluster

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items

Connection probabilities in Poisson random graphs with uniformly bounded edges

Cites Work

• Strict inequalities of critical values in continuum percolation
• Uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolation
• Uniqueness of unbounded occupied and vacant components in Boolean models
• Percolation and minimal spanning trees
• Probability on Graphs
• On the critical percolation probabilities
• Percolation
• On behaviour of automata in labyrinths
• Random Geometric Graphs
• Continuum Percolation
• Convex Analysis
• Probability
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