{"paper":{"title":"A BKR operation for events occurring for disjoint reasons with high probability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Larry Goldstein, Yosef Rinott","submitted_at":"2016-08-19T14:23:34Z","abstract_excerpt":"Given events $A$ and $B$ on a product space $S=\\prod_{i=1}^n S_i$, the set $A \\Box B$ consists of all vectors ${\\bf x}=(x_1,\\ldots,x_n) \\in S$ for which there exist disjoint coordinate subsets $K$ and $L$ of $\\{1,\\ldots,n\\}$ such that given the coordinates $x_i, i \\in K$ one has that ${\\bf x} \\in A$ regardless of the values of ${\\bf x}$ on the remaining coordinates, and likewise that ${\\bf x} \\in B$ given the coordinates {$x_j, j \\in L$}.\n  For a finite product of discrete spaces endowed with a product measure, the BKR inequality\n  $$\n  P(A \\Box B) \\le P(A)P(B) \\quad (1)\n  $$\n  was conjectured"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05612","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"}