{"paper":{"title":"Random walks on nilpotent groups driven by measures supported on powers of generators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.GR"],"primary_cat":"math.PR","authors_text":"Laurent Saloff-Coste, Tianyi Zheng","submitted_at":"2012-11-13T14:40:36Z","abstract_excerpt":"We study the decay of convolution powers of a large family $\\mu_{S,a}$ of measures on finitely generated nilpotent groups. Here, $S=(s_1,...,s_k)$ is a generating $k$-tuple of group elements and $a= (\\alpha_1,...,\\alpha_k)$ is a $k$-tuple of reals in the interval $(0,2)$. The symmetric measure $\\mu_{S,a}$ is supported by $S^*=\\{s_i^{m}, 1\\le i\\le k,\\,m\\in \\mathbb Z\\}$ and gives probability proportional to $$(1+m)^{-\\alpha_i-1}$$ to $s_i^{\\pm m}$, $i=1,...,k,$ $m\\in \\mathbb N$. We determine the behavior of the probability of return $\\mu_{S,a}^{(n)}(e)$ as $n$ tends to infinity. This behavior de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3003","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"}