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

Erwin Bolthausen; Taizo Chiyonobu; Tadahisa Funaki

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

机译：在存在两个可能的候选者的情况下弱固定高斯随机场的缩放极限

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摘要

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, for one dimensional fields to higher dimensions: d ≥ 3, at least if the strength of pinning is sufficiently large.

机译：我们研究了标度极限，并证明了在弱偏差高斯随机场的大数定律下，在大偏差原理水平存在极限的两个可能候选的情况下。本文将一维场的结果扩展到更高的维数：d≥3，至少是在钉扎强度足够大的情况下。

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来源
《Journal of the Mathematical Society of Japan》 |2015年第4期|1359-1412|共54页
作者
Erwin Bolthausen; Taizo Chiyonobu; Tadahisa Funaki;
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作者单位

Institut fuer Mathematik Universitaet Zuerich Winterthurerstrasse 190 8057 Zuerich, Switzerland;

Department of Mathematics Kwansei-Gakuin University Sanda-city Hyogo 669-1337, Japan;

Graduate School of Mathematical Sciences The University of Tokyo Komaba Tokyo 153-8914, Japan;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Gaussian field; interface model; pinning; scaling limit; large deviation; minimizers;

机译：高斯场接口模型;固定缩放限制;偏差大;最小化器;

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1. Concentration under scaling limits for weakly pinned Gaussian random walks [J] . Bolthausen E, Funaki T, Otobe T Probability Theory and Related Fields . 2009,第3a4期

机译：弱固定高斯随机游动的缩放限制下的浓度
2. Concentration under scaling limits for weakly pinned Gaussian random walks [J] . Erwin Bolthausen, Tadahisa Funaki, Tatsushi Otobe Probability Theory and Related Fields . 2009,第sa3a4期

机译：弱固定高斯随机游动的缩放限制下的浓度
3. The effects of the one-step replica symmetry breaking on the Sherrington-Kirkpatrick spin glass model in the presence of random field with a joint Gaussian probability density function for the exchange interactions and random fields [J] . Hadjiagapiou Ioannis A., Velonakis Ioannis N. Physica, A. Statistical mechanics and its applications . 2018,第期

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4. Coupling conditionally independent submaps for large-scale 2.5D mapping with Gaussian Markov Random Fields [C] . Liye Sun, Teresa Vidal-Calleja, Jaime Valls Miro IEEE International Conference on Robotics and Automation . 2017

机译：使用高斯马尔可夫随机场耦合条件独立子图进行大规模2.5D映射
5. SELECTED TOPICS IN SPATIAL STATISTICAL ANALYSIS: NONSTATIONARY VECTOR KRIGING, LARGE SCALE CONDITIONAL SIMULATION OF THREE-DIMENSIONAL GAUSSIAN RANDOM FIELDS, AND HYPOTHESIS TESTING IN A CORRELATED RANDOM FIELD [D] . QUIMBY, WILLIAM F. 1986

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6. Graphical Model Selection for Gaussian Conditional Random Fields in the Presence of Latent Variables [O] . Benjamin Frot, Luke Jostins, Gilean McVean -1

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7. Scaling limits for weakly pinned Gaussian random fields under the presence of two possible candidates [O] . Erwin BOLTHAUSEN, Taizo CHIYONOBU, Tadahisa FUNAKI 2015

机译：在两种可能的候选人的存在下缩小脊状高斯随机字段的缩放限制
8. Some Central Limit Theorems for Markov Paths and Some Properties of Gaussian Random Fields [R] . Adler, R. J., Epstein, R. 1987

机译：马尔可夫路径的中心极限定理及高斯随机场的若干性质

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

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