{"paper":{"title":"Excited random walk with periodic cookies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gady Kozma, Igor Shinkar, Tal Orenshtein","submitted_at":"2013-11-28T22:59:38Z","abstract_excerpt":"In this paper we consider an excited random walk on $\\mathbb{Z}$ in identically piled periodic environment. This is a discrete time process on $\\mathbb{Z}$ defined by parameters $(p_1,\\dots p_M) \\in [0,1]^M$ for some positive integer $M$, where the walker upon the $i$-th visit to $z \\in \\mathbb{Z}$ moves to $z+1$ with probability $p_{i\\pmod M}$, and moves to $z-1$ with probability $1-p_{i \\pmod M}$. We give an explicit formula in terms of the parameters $(p_1,\\dots,p_M)$ which determines whether the walk is recurrent, transient to the left, or transient to the right. In particular, in the case"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7439","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"}