The van den Berg--Kesten--Reimer operator and inequality for infinite spaces

Abstract

We remove the hypothesis "$S$ is finite" from the BKR inequality for product measures on $S^d$, 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.

15 pages

References in corpus (2)

• Some people have all the luck
• Functional van den Berg-Kesten-Reimer Inequalities and their Duals, with Applications

Cited by in corpus (1)

• On the exponent governing the correlation decay of the Airy${}_1$ process