{"paper":{"title":"Invariance principle for variable speed random walks on trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anita Winter, Siva Athreya, Wolfgang L\\\"ohr","submitted_at":"2014-04-24T23:31:05Z","abstract_excerpt":"We consider stochastic processes on complete, locally compact tree-like metric spaces $(T,r)$ on their \"natural scale\" with boundedly finite speed measure $\\nu$. Given a triple $(T,r,\\nu)$ such a speed-$\\nu$ motion on $(T,r)$ can be characterized as the unique strong Markov process which if restricted to compact subtrees satisfies for all $x,y\\in T$ and all positive, bounded measurable $f$, \\[ \\mathbb{E}^x [ \\int^{\\tau_y}_0\\mathrm{d}s\\, f(X_s) ]\n  = 2\\int_T\\nu(\\mathrm{d}z)\\, r(y,c(x,y,z))f(z)\n  < \\infty, \\] where $c(x,y,z)$ denotes the branch point generated by $x,y,z$. If $(T,r)$ is a discret"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6290","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"}