{"paper":{"title":"The subcritical phase for a homopolymer model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hugo Panzo, Iddo Ben-Ari","submitted_at":"2018-03-25T20:43:24Z","abstract_excerpt":"We study a model of continuous-time nearest-neighbor random walk on $\\mathbb{Z}^d$ penalized by its occupation time at the origin, also known as a homopolymer. For a fixed real parameter $\\beta$ and time $t>0$, we consider the probability measure on paths of the random walk starting from the origin whose Radon-Nikodym derivative is proportional to the exponent of the product $\\beta$ times the occupation time at the origin up to time $t$. The case $\\beta>0$ was studied previously by Cranston and Molchanov arXiv:1508.06915. We consider the case $\\beta<0$, which is intrinsically different only wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09335","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"}