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2019 Probability to be positive for the membrane model in dimensions 2 and 3
Simon Buchholz, Jean-Dominique Deuschel, Noemi Kurt, Florian Schweiger
Electron. Commun. Probab. 24: 1-14 (2019). DOI: 10.1214/19-ECP245

Abstract

We consider the membrane model on a box $V_{N}\subset \mathbb{Z} ^{n}$ of size $(2N+1)^{n}$ with zero boundary condition in the subcritical dimensions $n=2$ and $n=3$. We show optimal estimates for the probability that the field is positive in a subset $D_{N}$ of $V_{N}$. In particular we obtain for $D_{N}=V_{N}$ that the probability to be positive on the entire domain is exponentially small and the rate is of the order of the surface area $N^{n-1}$.

Citation

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Simon Buchholz. Jean-Dominique Deuschel. Noemi Kurt. Florian Schweiger. "Probability to be positive for the membrane model in dimensions 2 and 3." Electron. Commun. Probab. 24 1 - 14, 2019. https://doi.org/10.1214/19-ECP245

Information

Received: 5 November 2018; Accepted: 23 May 2019; Published: 2019
First available in Project Euclid: 5 July 2019

zbMATH: 07088985
MathSciNet: MR3978693
Digital Object Identifier: 10.1214/19-ECP245

Subjects:
Primary: 60G15
Secondary: 60G60, 82B41

JOURNAL ARTICLE
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