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 | |
| Publication status | Published - 2015 |
| Externally published | Yes |
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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 journal › Article
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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
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 -