{"paper":{"title":"Favorite sites of randomly biased walks on a supercritical Galton-Watson tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dayue Chen, Lo\\\"ic de Raph\\'elis, Yueyun Hu","submitted_at":"2016-11-14T17:53:06Z","abstract_excerpt":"Erd\\H{o}s and R\\'ev\\'esz initiated the study of favorite sites by considering the one-dimensional simple random walk. We investigate in this paper the same problem for a class of null-recurrent randomly biased walks on a supercritical Gaton-Watson tree. We prove that there is some parameter $\\kappa \\in (1, \\infty]$ such that the set of the favorite sites of the biased walk is almost surely bounded in the case $\\kappa \\in (2, \\infty]$, tight in the case $\\kappa=2$, and oscillates between a neighborhood of the root and the boundary of the range in the case $\\kappa \\in (1, 2)$. Moreover, our resu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04497","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"}