{"paper":{"title":"A Property of Random Walks on a Cycle Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Yasunari Fukai, Yoshihiro Mizoguchi, Yuki Ikeda","submitted_at":"2015-01-21T06:16:27Z","abstract_excerpt":"We analyze the Hunter vs Rabbit game on graph, which is a kind of model of communication in an adhoc mobile network. Let $G$ be a cycle graph with $N$ nodes. The hunter can move from a vertex to another vertex on the graph along an edge. The rabbit can move to any vertex on graph at once. We formalized the game using the random walk framework. The strategy of the rabbit is formalized using a one dimensional random walk over $\\mathbb{Z}$. We classify strategies using the order $O(k^{-\\beta-1})$ of their Fourier transformation. We investigate lower bounds and upper bounds of a probability that t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05066","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"}