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

Erwin Bolthausen; Taizo Chiyonobu; Tadahisa Funaki

doi:10.2969/jmsj/06741359

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

Erwin Bolthausen, Taizo Chiyonobu, Tadahisa Funaki

Research output: Contribution to journal › Article › peer-review

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 ≥ 3, at least if the strength of pinning is sufficiently large.

Original language	English
Pages (from-to)	1359-1412
Number of pages	54
Journal	Journal of the Mathematical Society of Japan
Volume	67
Issue number	4
DOIs	https://doi.org/10.2969/jmsj/06741359
Publication status	Published - 2015
Externally published	Yes

Keywords

Gaussian field
Interface model
Large deviation
Minimizers
Pinning
Scaling limit

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.2969/jmsj/06741359

Cite this

@article{81b4afef7a6249079f2b2613f676fdfd,

title = "Scaling limits for weakly pinned Gaussian random fields under the presence of two possible candidates",

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 ≥ 3, at least if the strength of pinning is sufficiently large.",

keywords = "Gaussian field, Interface model, Large deviation, Minimizers, Pinning, Scaling limit",

author = "Erwin Bolthausen and Taizo Chiyonobu and Tadahisa Funaki",

note = "Publisher Copyright: {\textcopyright} 2015 The Mathematical Society of Japan.",

year = "2015",

doi = "10.2969/jmsj/06741359",

language = "English",

volume = "67",

pages = "1359--1412",

journal = "Journal of the Mathematical Society of Japan",

issn = "0025-5645",

publisher = "Mathematical Society of Japan - Kobe University",

number = "4",

}

TY - JOUR

T1 - Scaling limits for weakly pinned Gaussian random fields under the presence of two possible candidates

AU - Bolthausen, Erwin

AU - Chiyonobu, Taizo

AU - Funaki, Tadahisa

PY - 2015

Y1 - 2015

N2 - 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 ≥ 3, at least if the strength of pinning is sufficiently large.

AB - 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 ≥ 3, at least if the strength of pinning is sufficiently large.

KW - Gaussian field

KW - Interface model

KW - Large deviation

KW - Minimizers

KW - Pinning

KW - Scaling limit

UR - http://www.scopus.com/inward/record.url?scp=84947080733&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84947080733&partnerID=8YFLogxK

U2 - 10.2969/jmsj/06741359

DO - 10.2969/jmsj/06741359

M3 - Article

AN - SCOPUS:84947080733

VL - 67

SP - 1359

EP - 1412

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 4

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this