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

Alberto Gandolfi

doi:10.1007/978-981-15-0298-9_8

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

Alberto Gandolfi

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	Sojourns in Probability Theory and Statistical Physics - II - Brownian Web and Percolation, A Festschrift for Charles M. Newman
Editors	Vladas Sidoravicius
Publisher	Springer
Pages	186-207
Number of pages	22
ISBN (Print)	9789811502972
DOIs	https://doi.org/10.1007/978-981-15-0298-9_8
State	Published - 2019
Event	International Conference on Probability Theory and Statistical Physics, 2016 - Shanghai, China Duration: Mar 25 2016 → Mar 27 2016

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	299
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International Conference on Probability Theory and Statistical Physics, 2016
Country/Territory	China
City	Shanghai
Period	3/25/16 → 3/27/16

Keywords

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

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-981-15-0298-9_8

Cite this

Gandolfi, A. (2019). FKG (and Other Inequalities) from (Generalized and Approximate) FK Random Cluster 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 Statistics; Vol. 299). Springer. https://doi.org/10.1007/978-981-15-0298-9_8

FKG (and Other Inequalities) from (Generalized and Approximate) FK Random Cluster Representation (and Iterated Folding). / Gandolfi, Alberto.
Sojourns in Probability Theory and Statistical Physics - II - Brownian Web and Percolation, A Festschrift for Charles M. Newman. ed. / Vladas Sidoravicius. Springer, 2019. p. 186-207 (Springer Proceedings in Mathematics and Statistics; Vol. 299).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Gandolfi, A 2019, FKG (and Other Inequalities) from (Generalized and Approximate) FK Random Cluster 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. Springer Proceedings in Mathematics and Statistics, vol. 299, Springer, pp. 186-207, International Conference on Probability Theory and Statistical Physics, 2016, Shanghai, China, 3/25/16. https://doi.org/10.1007/978-981-15-0298-9_8

Gandolfi A. FKG (and Other Inequalities) from (Generalized and Approximate) FK Random Cluster Representation (and Iterated Folding). In Sidoravicius V, editor, Sojourns in Probability Theory and Statistical Physics - II - Brownian Web and Percolation, A Festschrift for Charles M. Newman. Springer. 2019. p. 186-207. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-981-15-0298-9_8

Gandolfi, Alberto. / FKG (and Other Inequalities) from (Generalized and Approximate) FK Random Cluster Representation (and Iterated Folding). Sojourns in Probability Theory and Statistical Physics - II - Brownian Web and Percolation, A Festschrift for Charles M. Newman. editor / Vladas Sidoravicius. Springer, 2019. pp. 186-207 (Springer Proceedings in Mathematics and Statistics).

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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.",

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

Abstract

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Keywords

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