{"paper":{"title":"A new approach to an old problem of Erdos and Moser","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hoi H. Nguyen","submitted_at":"2011-12-04T14:13:14Z","abstract_excerpt":"Let $\\eta_i, i=1,..., n$ be iid Bernoulli random variables, taking values $\\pm 1$ with probability 1/2. Given a multiset $V$ of $n$ elements $v_1, ..., v_n$ of an additive group $G$, we define the \\emph{concentration probability} of $V$ as\n  $$\\rho(V) := \\sup_{v\\in G} P(\\eta_1 v_1 + ... \\eta_n v_n =v). $$\n  An old result of Erdos and Moser asserts that if $v_i $ are distinct real numbers then $\\rho(V)$ is $O(n^{-3/2}\\log n)$. This bound was then refined by Sarkozy and Szemeredi to $O(n^{-3/2})$, which is sharp up to a constant factor. The ultimate result dues to Stanley who used tools from alg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0755","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"}