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

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arxiv 1508.05337 v3 pith:4AQX3RS7 submitted 2015-08-21 math.PR

Richard Arratia , Skip Garibaldi , Alfred W. Hales This is my paper · ORCID
classification math.PR
keywords inequalityeventsfinitehypothesisoperatorremoveberg--kesten--reimerdescriptive
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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.

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    In the regime d > min{6, 3alpha}, critical long-range percolation clusters have an n^{-1/2} volume tail and integrated superprocess scaling limits, switching from super-Levy (alpha < 2) to super-Brownian (alpha >= 2);...

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