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 journalArticle

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 languageEnglish
Pages (from-to)1359-1412
Number of pages54
JournalJournal of the Mathematical Society of Japan
Volume67
Issue number4
DOIs
Publication statusPublished - 2015
Externally publishedYes

Fingerprint

Gaussian Random Field
Large Deviation Principle
Law of large numbers
Scaling Limit
Higher Dimensions

Keywords

  • Gaussian field
  • Interface model
  • Large deviation
  • Minimizers
  • Pinning
  • Scaling limit

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Scaling limits for weakly pinned Gaussian random fields under the presence of two possible candidates. / Bolthausen, Erwin; Chiyonobu, Taizo; Funaki, Tadahisa.

In: Journal of the Mathematical Society of Japan, Vol. 67, No. 4, 2015, p. 1359-1412.

Research output: Contribution to journalArticle

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