{"paper":{"title":"Local limit theorem for symmetric random walks in Gromov-hyperbolic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Sebastien Gouezel (IRMAR)","submitted_at":"2012-09-14T15:07:31Z","abstract_excerpt":"Completing a strategy of Gou\\\"ezel and Lalley, we prove a local limit theorem for the random walk generated by any symmetric finitely supported probability measure on a non-elementary Gromov-hyperbolic group: denoting by $R$ the inverse of the spectral radius of the random walk, the probability to return to the identity at time $n$ behaves like $C R^{-n}n^{-3/2}$. An important step in the proof is to extend Ancona's results on the Martin boundary up to the spectral radius: we show that the Martin boundary for $R$-harmonic functions coincides with the geometric boundary of the group. In an appe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3217","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"}