Entropic repulsion and scaling limit for a finite number of non-intersecting subcritical FK interfaces
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916820103987200 |
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| author | D'Alimonte, Lucas |
| author_facet | D'Alimonte, Lucas |
| contents | This article is devoted to the study of a finite system of long clusters of subcritical 2-dimensional FK-percolation with q $\geq$ 1, conditioned on mutual avoidance. We show that the diffusive scaling limit of such a system is given by a system of Brownian bridges conditioned not to intersect: the so-called Brownian watermelon. Moreover, we give an estimate of the probability that two sets of $r$ points at distance $n$ of each other are connected by distinct clusters. As a byproduct, we obtain the asymptotics of the probability of the occurrence of a large finite cluster in a supercritical random-cluster model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_14767 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Entropic repulsion and scaling limit for a finite number of non-intersecting subcritical FK interfaces D'Alimonte, Lucas Probability Mathematical Physics 60K35, 82B20, 82B41, 82B43 This article is devoted to the study of a finite system of long clusters of subcritical 2-dimensional FK-percolation with q $\geq$ 1, conditioned on mutual avoidance. We show that the diffusive scaling limit of such a system is given by a system of Brownian bridges conditioned not to intersect: the so-called Brownian watermelon. Moreover, we give an estimate of the probability that two sets of $r$ points at distance $n$ of each other are connected by distinct clusters. As a byproduct, we obtain the asymptotics of the probability of the occurrence of a large finite cluster in a supercritical random-cluster model. |
| title | Entropic repulsion and scaling limit for a finite number of non-intersecting subcritical FK interfaces |
| topic | Probability Mathematical Physics 60K35, 82B20, 82B41, 82B43 |
| url | https://arxiv.org/abs/2307.14767 |