{"paper":{"title":"Infinite Volume Continuum Random Cluster Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Dereudre, Pierre Houdebert","submitted_at":"2015-07-10T13:26:19Z","abstract_excerpt":"The continuum random cluster model is defined as a Gibbs modification of the stationary Boolean model in $\\mathbb{R}^d$ with intensity $z>0$ and the law of radii $Q$. The formal unormalized density is given by $q^{N_{cc}}$ where $q>0$ is a fixed parameter and $N_{cc}$ the number of connected components in the random germ-grain structure. In this paper we prove the existence of the model in the infinite volume regime for a large class of parameters including the case $q<1$ or distributions $Q$ without compact support. In the extreme setting of non integrable radii (i.e. $\\int R^d Q(dR)=\\infty$)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02891","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}