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Influence in product spaces
Univ Cambridge, Stat Lab, Ctr Math Sci, Wilberforce Rd, Cambridge CB3 0WB, England..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Univ Cambridge, Stat Lab, Ctr Math Sci, Wilberforce Rd, Cambridge CB3 0WB, England..
2016 (English)In: Advances in Applied Probability, ISSN 0001-8678, E-ISSN 1475-6064, Vol. 48, no A, 145-152 p.Article in journal (Refereed) Published
Abstract [en]

The theory of influence and sharp threshold is a key tool in probability and probabilistic combinatorics, with numerous applications. One significant aspect of the theory is directed at identifying the level of generality of the product probability space that accommodates the event under study. We derive the influence inequality for a completely general product space, by establishing a relationship to the Lebesgue cube studied by Bourgain, Kahn, Kalai, Katznelson and Linial (BKKKL) in 1992. This resolves one of the assertions of BKKKL. Our conclusion is valid also in the setting of the generalized influences of Keller.

Place, publisher, year, edition, pages
2016. Vol. 48, no A, 145-152 p.
Keyword [en]
Influence, sharp threshold, product space, separable space, measure-space isomorphism
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-311243DOI: 10.1017/apr.2016.46ISI: 000388296000009OAI: oai:DiVA.org:uu-311243DiVA: diva2:1059417
Funder
Knut and Alice Wallenberg Foundation
Available from: 2016-12-22 Created: 2016-12-22 Last updated: 2016-12-22Bibliographically approved

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