Entropic repulsion and scaling limit for a finite number of non-intersecting subcritical FK interfaces

Lucas D’Alimonte

doi:10.1214/24-EJP1127

2024 Entropic repulsion and scaling limit for a finite number of non-intersecting subcritical FK interfaces

Lucas D’Alimonte

Author Affiliations +

Electron. J. Probab. 29: 1-53 (2024). DOI: 10.1214/24-EJP1127

Abstract

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.

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Lucas D’Alimonte "Entropic repulsion and scaling limit for a finite number of non-intersecting subcritical FK interfaces," Electronic Journal of Probability 29(none), 1-53, (2024). https://doi.org/10.1214/24-EJP1127

Received: 15 September 2023; Accepted: 16 April 2024; Published: 2024

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