### 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.

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 |

Subtitle of host publication | A Festschrift for Charles M. Newman |

Editors | Vladas Sidoravicius |

Place of Publication | Singapore |

Publisher | Springer New York |

Pages | 186-207 |

Number of pages | 21 |

ISBN (Electronic) | 978-981-15-0298-9 |

ISBN (Print) | 978-981-15-0297-2 |

State | Published - 2019 |

### Publication series

Name | Springer Proceedings in Mathematics and Physics |
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### 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.