{"paper":{"title":"Gibbs States on Random Configurations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alexei Daletskii, Tanja Pasurek, Yuri Kondratiev, Yuri Kozitsky","submitted_at":"2013-07-17T18:26:23Z","abstract_excerpt":"We study a class of Gibbs measures of classical particle spin systems with spin space $S=\\mathbb{R}^{m}$ and unbounded pair interaction, living on a metric graph given by a typical realization $\\gamma $ of a random point process in $\\mathbb{R}^{n}$. Under certain conditions of growth of pair- and self-interaction potentials, we prove that the set $\\mathcal{G}(S^{\\gamma})$ of all such Gibbs measures is not empty for almost all $\\gamma $, and study support properties of $\\nu_{\\gamma}\\in \\mathcal{G}(S^{\\gamma})$. Moreover we show the existence of measurable maps (selections) $\\gamma \\mapsto \\nu_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4718","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"}