{"paper":{"title":"Random walks under slowly varying moment conditions on groups of polynomial volume growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Laurent Saloff-Coste, Tianyi Zheng","submitted_at":"2015-07-13T19:03:25Z","abstract_excerpt":"Let $G$ be a finitely generated group of polynomial volume growth equipped with a word-length $|\\cdot|$. The goal of this paper is to develop techniques to study the behavior of random walks driven by symmetric measures $\\mu$ such that, for any $\\epsilon>0$, $\\sum|\\cdot|^\\epsilon\\mu=\\infty$. In particular, we provide a sharp lower bound for the return probability in the case when $\\mu$ has a finite weak-logarithmic moment."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03551","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"}