{"paper":{"title":"A general renormalization procedure on the one-dimensional lattice and decay of correlations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","math.PR"],"primary_cat":"math.DS","authors_text":"Artur O. Lopes","submitted_at":"2017-01-26T11:17:26Z","abstract_excerpt":"We present a general form of Renormalization operator $\\mathcal{R}$ acting on potentials $V:\\{0,1\\}^\\mathbb{N} \\to \\mathbb{R}$. We exhibit the analytical expression of the fixed point potential $V$ for such operator $\\mathcal{R}$. This potential can be expressed in a naturally way in terms of a certain integral over the Hausdorff probability on a Cantor type set on the interval $[0,1]$. This result generalizes a previous one by A. Baraviera, R. Leplaideur and A. Lopes where the fixed point potential $V$ was of Hofbauer type.\n  For the potentials of Hofbauer type (a well known case of phase tra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07656","kind":"arxiv","version":3},"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"}