Influence in product spaces
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
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.
Influence, sharp threshold, product space, separable space, measure-space isomorphism
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:uu:diva-311243DOI: 10.1017/apr.2016.46ISI: 000388296000009OAI: oai:DiVA.org:uu-311243DiVA: diva2:1059417
FunderKnut and Alice Wallenberg Foundation