TY - GEN

T1 - FKG (and Other Inequalities) from (Generalized and Approximate) FK Random Cluster Representation (and Iterated Folding)

AU - Gandolfi, Alberto

N1 - Publisher Copyright:
© Springer Nature Singapore Pte Ltd. 2019.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Approximate random cluster representation

KW - FK

KW - FKG

KW - Folding

KW - Negative association

KW - Positive association

KW - Random cluster representation

KW - Tree

UR - http://www.scopus.com/inward/record.url?scp=85085737171&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85085737171&partnerID=8YFLogxK

U2 - 10.1007/978-981-15-0298-9_8

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

M3 - Conference contribution

AN - SCOPUS:85085737171

SN - 9789811502972

T3 - Springer Proceedings in Mathematics and Statistics

SP - 186

EP - 207

BT - Sojourns in Probability Theory and Statistical Physics - II - Brownian Web and Percolation, A Festschrift for Charles M. Newman

A2 - Sidoravicius, Vladas

PB - Springer

T2 - International Conference on Probability Theory and Statistical Physics, 2016

Y2 - 25 March 2016 through 27 March 2016

ER -