{"paper":{"title":"Gibbs measures over locally tree-like graphs and percolative entropy over infinite regular trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Moumanti Podder, Tim Austin","submitted_at":"2017-05-10T02:29:02Z","abstract_excerpt":"Consider a statistical physical model on the $d$-regular infinite tree $T_{d}$ described by a set of interactions $\\Phi$. Let $\\{G_{n}\\}$ be a sequence of finite graphs with vertex sets $V_n$ that locally converge to $T_{d}$. From $\\Phi$ one can construct a sequence of corresponding models on the graphs $G_n$. Let $\\{\\mu_n\\}$ be the resulting Gibbs measures. Here we assume that $\\{\\mu_{n}\\}$ converges to some limiting Gibbs measure $\\mu$ on $T_{d}$ in the local weak$^*$ sense, and study the consequences of this convergence for the specific entropies $|V_n|^{-1}H(\\mu_n)$. We show that the limit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03589","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"}