### 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) |
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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 | |

State | Published - Jan 1 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 |
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Volume | 299 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Conference

Conference | International Conference on Probability Theory and Statistical Physics, 2016 |
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Country | 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

- Mathematics(all)

## Fingerprint Dive into the research topics of 'FKG (and Other Inequalities) from (Generalized and Approximate) FK Random Cluster Representation (and Iterated Folding)'. Together they form a unique fingerprint.

## 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