{"paper":{"title":"Inverse Littlewood-Offord problems for Quasi-Norms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ohad Giladi, Olivier Gu\\'edon, Omer Friedland","submitted_at":"2015-10-14T00:33:25Z","abstract_excerpt":"Given a star-shaped domain $K\\subseteq \\mathbb R^d$, $n$ vectors $v_1,\\dots,v_n \\in \\mathbb R^d$, a number $R>0$, and i.i.d. random variables $\\eta_1,\\dots,\\eta_n$, we study the geometric and arithmetic structure of the set of vectors $V = \\{v_1,\\dots,v_n\\}$ under the assumption that the small ball probability \\[\\sup_{x\\in \\mathbb R^d}~\\mathbb P\\Bigg(\\sum_{j=1}^n\\eta_jv_j\\in x+RK\\Bigg)\\] does not decay too fast as $n\\to \\infty$. This generalises the case where $K$ is the Euclidean ball, which was previously studied by Nguyen-Vu and Tao-Vu."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03937","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"}