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

1 Citation (Scopus)

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)

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

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

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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

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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