FKG (and Other Inequalities) from (Generalized and Approximate) FK Random Cluster Representation (and Iterated Folding)

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper we prove several inequalities by means of diagrammatic expansions, a technique already used in [1]. This time we show that iterations of the folding of a probability leads to the proof of some inequalities by means of a generalized and approximate random cluster representation of the iterated foldings. One of the inequalities is the well known FKG inequality, which ends up being proven, quite unexpectedly, by means of the (generalized) FK representation. Although most of the results are not new, we hope that the techniques will find applications in other contexts.

Original languageEnglish (US)
Title of host publicationSojourns in Probability Theory and Statistical Physics - II - Brownian Web and Percolation, A Festschrift for Charles M. Newman
EditorsVladas Sidoravicius
PublisherSpringer
Pages186-207
Number of pages22
ISBN (Print)9789811502972
DOIs
StatePublished - 2019
EventInternational Conference on Probability Theory and Statistical Physics, 2016 - Shanghai, China
Duration: Mar 25 2016Mar 27 2016

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume299
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceInternational Conference on Probability Theory and Statistical Physics, 2016
CountryChina
CityShanghai
Period3/25/163/27/16

Keywords

  • Approximate random cluster representation
  • FK
  • FKG
  • Folding
  • Negative association
  • Positive association
  • Random cluster representation
  • Tree

ASJC Scopus subject areas

  • Mathematics(all)

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