Msr - Tr - 98 - 42 the Van Den Berg - Kesten - Reimer Inequality : a Review
نویسندگان
چکیده
We present a variant of Reimer’s proof of the van den Berg-Kesten conjecture.
منابع مشابه
The Van Den Berg–kesten–reimer Operator and Inequality for Infinite Spaces
We remove the hypothesis “S is finite” from the BKR inequality for product measures on Sd, which raises some issues related to descriptive set theory. We also discuss the extension of the BKR operator and inequality, from 2 events to 2 or more events, and we remove, in one sense, the hypothesis that d be finite.
متن کاملClosure Properties and Negatively Associated Measures Violating the Van Den Berg-kesten Inequality
We first give an example of a negatively associated measure which does not satisfy the van den Berg-Kesten inequality. Next we show that the class of measures satisfying the van den BergKesten inequality is not closed under either of conditioning, introduction of external fields or convex combinations. Finally we show that this class also includes measure which have rank sequence which is not l...
متن کاملFunctional van den Berg-Kesten-Reimer Inequalities and their Duals, with Applications
The BKR inequality conjectured by van den Berg and Kesten in [11], and proved by Reimer in [8], states that for A and B events on S, a finite product of finite sets Si, i = 1, . . . , n, and P any product measure on S, P (A B) ≤ P (A)P (B), where the set A B consists of the elementary events which lie in both A and B for ‘disjoint reasons.’ Precisely, with n := {1, . . . , n} and K ⊂ n, for x ∈...
متن کاملA Dual Version of Reimer's Inequality and a Proof of Rudich's Conjecture
We prove a dual version of the celebrated inequality of D. Reimer (a.k.a. the van den Berg-Kesten conjecture). We use the dual inequality to prove a combinatorial conjecture of S. Rudich motivated by questions in cryptographic complexity. One consequence of Rudich’s Conjecture is that there is an oracle relative to which one-way functions exist but one-way permutations do not. The dual inequali...
متن کاملReimer's Inequality on a Finite Distributive Lattice
We generalize Reimer’s Inequality [6] (a.k.a the BKR Inequality or the van den Berg–Kesten Conjecture [1]) to the setting of finite distributive lattices. (MSC 60C05)
متن کامل