{"paper":{"title":"On large deviations for the cover time of two-dimensional torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christophe Gallesco, Francis Comets, Marina Vachkovskaia, Serguei Popov","submitted_at":"2013-06-21T22:17:15Z","abstract_excerpt":"Let $\\mathcal{T}_n$ be the cover time of two-dimensional discrete torus $\\mathbb{Z}^2_n=\\mathbb{Z}^2/n\\mathbb{Z}^2$. We prove that $\\mathbb{P}[\\mathcal{T}_n\\leq \\frac{4}{\\pi}\\gamma n^2\\ln^2 n]=\\exp(-n^{2(1-\\sqrt{\\gamma})+o(1)})$ for $\\gamma\\in (0,1)$. One of the main methods used in the proofs is the decoupling of the walker's trace into independent excursions by means of soft local times."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5266","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"}