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 |
Keywords
- Gaussian field
- Interface model
- Large deviation
- Minimizers
- Pinning
- Scaling limit
ASJC Scopus subject areas
- Mathematics(all)
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Cite this
Bolthausen, E., Chiyonobu, T., & Funaki, T. (2015). Scaling limits for weakly pinned Gaussian random fields under the presence of two possible candidates. Journal of the Mathematical Society of Japan, 67(4), 1359-1412. https://doi.org/10.2969/jmsj/06741359