{"paper":{"title":"Random Walk on Random Walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Augusto Teixeira, Frank den Hollander, Marcelo Hil\\'ario, Renato Soares dos Santos, Vladas Sidoravicius","submitted_at":"2014-01-18T00:20:27Z","abstract_excerpt":"In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density $\\rho \\in (0,\\infty)$. At each step the random walk performs a nearest-neighbour jump, moving to the right with probability $p_{\\circ}$ when it is on a vacant site and probability $p_{\\bullet}$ when it is on an occupied site. Assuming that $p_\\circ \\in (0,1)$ and $p_\\bullet \\neq \\tfrac12$, we show that the position of the random walk satisfies a strong law of large numbers, a funct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4498","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"}