{"paper":{"title":"Collisions of several walkers in recurrent random environments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexis Devulder (LMV), Fran\\c{c}oise Pene (LMBA), Nina Gantert","submitted_at":"2018-07-11T09:20:32Z","abstract_excerpt":"We consider d independent walkers on Z, m of them performing simple symmetric random walk and r = d -- m of them performing recurrent RWRE (Sinai walk), in I independent random environments. We show that the product is recurrent, almost surely, if and only if m $\\le$ 1 or m = d = 2. In the transient case with r $\\ge$ 1, we prove that the walkers meet infinitely often, almost surely, if and only if m = 2 and r $\\ge$ I = 1. In particular, while I does not have an influence for the recurrence or transience, it does play a role for the probability to have infinitely many meetings. To obtain these "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04019","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"}