Proof of the Van den Berg–Kesten Conjecture

Authors:
David Reimer
Affiliations:
Dept. of Mathematics, The College of New Jersey, Ewing, NJ 08628-0718, USA (e-mail: dreimer@tcnj.edu)
Venue:
Combinatorics, Probability and Computing
Year:
2000

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Abstract

We prove the following conjecture of J. van den Berg and H. Kesten.For any events 𝒜 and ℬ in a product probabilityspace, Prob(𝒜□ℬ) ≤Prob(𝒜)Prob(ℬ), where 𝒜□ℬis the event that 𝒜 and ℬ occur disjointly.