INFLUENCE IN PRODUCT SPACES
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Grimmett, Geoffrey R
Janson, Svante
Norris, James R
Abstract
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.
Description
Keywords
Influence, sharp threshold, product space, separable space, measure-space isomorphism
Journal Title
ADVANCES IN APPLIED PROBABILITY
Conference Name
Journal ISSN
0001-8678
1475-6064
1475-6064
Volume Title
48
Publisher
Cambridge University Press (CUP)
Publisher DOI
Rights
All rights reserved
Sponsorship
Engineering and Physical Sciences Research Council (EP/I03372X/1)