Abstract
Abstract
The continuum random cluster model is a Gibbs modification of the standard Boolean model with intensity z > 0 and law of radii Q. The formal unnormalised density is given by q
N
cc
, where q is a fixed parameter and N
cc is the number of connected components in the random structure. We prove for a large class of parameters that percolation occurs for large enough z and does not occur for small enough z. We provide an application to the phase transition of the Widom–Rowlinson model with random radii. Our main tools are stochastic domination properties, a detailed study of the interaction of the model, and a Fortuin–Kasteleyn representation.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Sharp phase transition for the continuum Widom–Rowlinson model;Annales de l'Institut Henri Poincaré, Probabilités et Statistiques;2021-02-01
2. Disagreement percolation for Gibbs ball models;Stochastic Processes and their Applications;2019-10
3. Phase Transition for Continuum Widom–Rowlinson Model with Random Radii;Journal of Statistical Physics;2018-10-20