{"paper":{"title":"Brownian motion on treebolic space: escape to infinity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GR"],"primary_cat":"math.PR","authors_text":"Alexander Bendikov, Laurent Saloff-Coste, Maura Salvatori, Wolfgang Woess","submitted_at":"2012-12-26T10:12:25Z","abstract_excerpt":"Treebolic space is an analog of the Sol geometry, namely, it is the horocylic product of the hyperbolic upper half plane H and the homogeneous tree T with degree p+1 > 2, the latter seen as a one-complex. Let h be the Busemann function of T with respect to a fixed boundary point. Then for real q > 1 and integer p > 1, treebolic space HT(q,p) consists of all pairs (z=x+i y,w) in H x T with h(w) = log_{q} y. It can also be obtained by glueing together horziontal strips of H in a tree-like fashion. We explain the geometry and metric of HT and exhibit a locally compact group of isometries (a horoc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6151","kind":"arxiv","version":4},"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"}