{"paper":{"title":"The Littlewood-Offord Problem for Markov Chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.PR"],"primary_cat":"math.CO","authors_text":"Shravas Rao","submitted_at":"2019-04-30T02:22:39Z","abstract_excerpt":"The celebrated Littlewood-Offord problem asks for an upper bound on the probability that the random variable $\\epsilon_1 v_1 + \\cdots + \\epsilon_n v_n$ lies in the Euclidean unit ball, where $\\epsilon_1, \\ldots, \\epsilon_n \\in \\{-1, 1\\}$ are independent Rademacher random variables and $v_1, \\ldots, v_n \\in \\mathbb{R}^d$ are fixed vectors of at least unit length.We extend many known results to the case that the $\\epsilon_i$ are obtained from a Markov chain, including the general bounds first shown by Erd\\H{o}s in the scalar case and Kleitman in the vector case, and also under the restriction th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.13019","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"}