Wetting Transition on Trees I: Percolation With Clustering
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866918090796695552 |
|---|---|
| author | Cortines, Aser Harel, Itamar Ioffe, Dmitry Louidor, Oren |
| author_facet | Cortines, Aser Harel, Itamar Ioffe, Dmitry Louidor, Oren |
| contents | A new ``Percolation with Clustering'' (PWC) model is introduced, where (the probabilities of) site percolation configurations on the leaf set of a binary tree are rewarded exponentially according to a generic function, which measures the degree of clustering in the configuration. Conditions on such ``clustering function'' are given for the existence of a limiting free energy and a wetting transition, namely the existence of a non-trivial percolation parameter threshold above and only above which the set of ``dry'' (open) sites have an asymptotic density. Several examples of clustering functions are given and studied using the general theory. The results here will be used in a sequel paper to study the wetting transition for the discrete Gaussian free field on the tree subject to a hard wall constraint. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13551 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Wetting Transition on Trees I: Percolation With Clustering Cortines, Aser Harel, Itamar Ioffe, Dmitry Louidor, Oren Probability Mathematical Physics 82B41, 82B26, 82B05 A new ``Percolation with Clustering'' (PWC) model is introduced, where (the probabilities of) site percolation configurations on the leaf set of a binary tree are rewarded exponentially according to a generic function, which measures the degree of clustering in the configuration. Conditions on such ``clustering function'' are given for the existence of a limiting free energy and a wetting transition, namely the existence of a non-trivial percolation parameter threshold above and only above which the set of ``dry'' (open) sites have an asymptotic density. Several examples of clustering functions are given and studied using the general theory. The results here will be used in a sequel paper to study the wetting transition for the discrete Gaussian free field on the tree subject to a hard wall constraint. |
| title | Wetting Transition on Trees I: Percolation With Clustering |
| topic | Probability Mathematical Physics 82B41, 82B26, 82B05 |
| url | https://arxiv.org/abs/2410.13551 |