{"paper":{"title":"Exponential decay of connectivity and uniqueness in percolation on finite and infinite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.MP"],"primary_cat":"math-ph","authors_text":"Kathleen E. Hamilton, Leonid P. Pryadko","submitted_at":"2016-10-16T18:28:10Z","abstract_excerpt":"We give an upper bound for the uniqueness transition on an arbitrary locally finite graph ${\\cal G}$ in terms of the limit of the spectral radii $\\rho\\left[ H({\\cal G}_t)\\right]$ of the non-backtracking (Hashimoto) matrices for an increasing sequence of subgraphs ${\\cal G}_t\\subset{\\cal G}_{t+1}$ which converge to ${\\cal G}$. With the added assumption of strong local connectivity for the oriented line graph (OLG) of ${\\cal G}$, connectivity on any finite subgraph ${\\cal G}'\\subset{\\cal G}$ decays exponentially for $p<(\\rho\\left[ H({\\cal G}^{\\prime})\\right])^{-1}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04897","kind":"arxiv","version":1},"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"}