Journal of the Mathematical Society of Japan

Scaling limits for weakly pinned Gaussian random fields under the presence of two possible candidates

Erwin BOLTHAUSEN, Taizo CHIYONOBU, and Tadahisa FUNAKI

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Abstract

We study the scaling limit and prove the law of large numbers for weakly pinned Gaussian random fields under the critical situation that two possible candidates of the limits exist at the level of large deviation principle. This paper extends the results of [3], [7] for one dimensional fields to higher dimensions: $d\ge3 $, at least if the strength of pinning is sufficiently large.

Article information

Source
J. Math. Soc. Japan, Volume 67, Number 4 (2015), 1359-1412.

Dates
First available in Project Euclid: 27 October 2015

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1445951154

Digital Object Identifier
doi:10.2969/jmsj/06741359

Mathematical Reviews number (MathSciNet)
MR3417501

Zentralblatt MATH identifier
1334.60205

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60F10: Large deviations 82B41: Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41]

Keywords
Gaussian field interface model pinning scaling limit large deviation minimizers

Citation

BOLTHAUSEN, Erwin; CHIYONOBU, Taizo; FUNAKI, Tadahisa. Scaling limits for weakly pinned Gaussian random fields under the presence of two possible candidates. J. Math. Soc. Japan 67 (2015), no. 4, 1359--1412. doi:10.2969/jmsj/06741359. https://projecteuclid.org/euclid.jmsj/1445951154


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