{"paper":{"title":"Random walks driven by low moment measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Bendikov, Laurent Saloff-Coste","submitted_at":"2012-10-29T13:33:03Z","abstract_excerpt":"We study the decay of convolution powers of probability measures without second moment but satisfying some weaker finite moment condition. For any locally compact unimodular group G and any positive function $\\rho:G \\rightarrow [0,+\\infty]$, we introduce a function $\\Phi_{G,\\rho}$ which describes the fastest possible decay of $n \\mapsto \\phi^{(2n)}(e)$ when \\phi is a symmetric continuous probability density such that $\\int\\rho\\phi$ is finite. We estimate $\\Phi_{G,\\rho}$ for a variety of groups G and functions \\rho. When \\rho is of the form $\\rho=\\rho \\circ \\delta$ with $\\rho:[0,+\\infty) \\right"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7658","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"}