FKG (and other inequalities) via (generalized) FK representation (and iterated folding)

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

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
Subtitle of host publicationA Festschrift for Charles M. Newman
EditorsVladas Sidoravicius
Place of PublicationSingapore
PublisherSpringer New York
Pages186-207
Number of pages21
ISBN (Electronic)978-981-15-0298-9
ISBN (Print)978-981-15-0297-2
StatePublished - 2019

Publication series

NameSpringer Proceedings in Mathematics and Physics

Keywords

  • FK clusters
  • Random cluster representation
  • FKG inequality
  • Positive Association
  • Negative association property
  • Approximate Random Cluster Representation
  • Folding
  • Tree

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  • Cite this

    Gandolfi, A. (2019). FKG (and other inequalities) via (generalized) FK representation (and iterated folding). In V. Sidoravicius (Ed.), Sojourns in Probability Theory and Statistical Physics - II Brownian Web and Percolation: A Festschrift for Charles M. Newman (pp. 186-207). (Springer Proceedings in Mathematics and Physics). Springer New York.