{"paper":{"title":"Random Walks in I.I.D. Random Environment on Cayley Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Amites Dasgupta, Antar Bandyopadhyay, Siva Athreya","submitted_at":"2013-07-12T07:45:56Z","abstract_excerpt":"We consider the random walk in an \\emph{i.i.d.} random environment on the infinite $d$-regular tree for $d \\geq 3$. We consider the tree as a Cayley graph of free product of finitely many copies of $\\Zbold$ and $\\Zbold_2$ and define the i.i.d. environment as invariant under the action of this group. Under a mild non-degeneracy assumption we show that the walk is always transient."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3353","kind":"arxiv","version":2},"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"}