Invariance Principle for a Potts Interface Along a Wall

Ioffe, Dmitry; Ott, Sébastien; Velenik, Yvan; Wachtel, Vitali

doi:10.1007/s10955-020-02546-8

Scientific article

English

Invariance Principle for a Potts Interface Along a Wall

ContributorsIoffe, Dmitry; Ott, Sébastien; Velenik, Yvan

; Wachtel, Vitali

Published inJournal of Statistical Physics, no. 180, p. 832-861

Publication date2020

Abstract

We consider nearest-neighbor two-dimensional Potts models, with boundary conditions leading to the presence of an interface along the bottom wall of the box. We show that, after a suitable diffusive scaling, the interface weakly converges to the standard Brownian excursion.

Keywords

Potts model
Random cluster model
Interface
Ornstein-Zernike asymptotics
Invariance principle
Brownian excursion

Classification

arxiv : math.PR

Affiliation entities

Faculté des sciences / Section de mathématiques

Citation (ISO format)

IOFFE, Dmitry et al. Invariance Principle for a Potts Interface Along a Wall. In: Journal of Statistical Physics, 2020, n° 180, p. 832–861. doi: 10.1007/s10955-020-02546-8

Article (Submitted version)

Article (Published version)

Identifiers

PID : unige:128933
DOI : 10.1007/s10955-020-02546-8
arXiv : 2001.04737

Journal ISSN0022-4715

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106downloads

Creation15/01/2020 08:46:00

First validation15/01/2020 08:46:00

Update time15/03/2023 18:45:18

Status update15/03/2023 18:45:16

Last indexation31/10/2024 17:35:48

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Invariance Principle for a Potts Interface Along a Wall

We consider nearest-neighbor two-dimensional Potts models, with boundary conditions leading to the presence of an interface along the bottom wall of the box. We show that, after a suitable diffusive scaling, the interface weakly converges to the standard Brownian excursion.

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