{"paper":{"title":"On the Critical Behavior of a Homopolymers Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Michael Cranston, Stanislav Molchanov","submitted_at":"2015-08-27T16:09:16Z","abstract_excerpt":"Taking $P^0$ to be the measure induced by simple, symmetric nearest neighbor continuous time random walk on ${\\bf{Z^d}}$ starting at $0$ with jump rate $2d$ define, for $\\beta\\ge 0,\\,t>0,$ the Gibbs probability measure $P_{\\beta,t}$ by specifying its density with respect to $P^0$ as \\begin{eqnarray} \\frac{dP_{\\beta,t}}{dP^0}=Z_{\\beta,t}(0)^{-1}e^{\\beta \\int_0^t\\delta_0(x_s)ds} \\end{eqnarray} where $Z_{\\beta,t}(0)\\equiv E^0[e^{\\beta \\int_0^t\\delta_0(x_s)ds}].$ This Gibbs probability measure provides a simple model for a homopolymer with an attractive potential at the origin. In a previous paper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06915","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"}