{"paper":{"title":"Behaviors of entropy on finitely generated groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.GR","authors_text":"J\\'er\\'emie Brieussel","submitted_at":"2011-10-23T23:48:57Z","abstract_excerpt":"A variety of behaviors of entropy functions of random walks on finitely generated groups is presented, showing that for any $\\frac{1}{2}\\leq \\alpha\\leq\\beta\\leq1$, there is a group $\\Gamma$ with measure $\\mu$ equidistributed on a finite generating set such that \\[\\liminf\\frac{\\log H_{\\Gamma ,\\mu}(n)}{\\log n}=\\alpha ,\\qquad \\limsup \\frac{\\log H_{\\Gamma ,\\mu}(n)}{\\log n}=\\beta .\\] The groups involved are finitely generated subgroups of the group of automorphisms of an extended rooted tree. The return probability and the drift of a simple random walk $Y_n$ on such groups are also evaluated, provi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5099","kind":"arxiv","version":3},"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"}