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Concentration under scaling limits for weakly pinned Gaussian random walks


Bolthausen, E; Funaki, T; Otobe, T (2009). Concentration under scaling limits for weakly pinned Gaussian random walks. Probability Theory and Related Fields, 143(3-4):441-480.

Abstract

We study scaling limits for d-dimensional Gaussian random walks perturbed by an attractive force toward a certain subspace of $$\mathbb {R}^d$$, especially under the critical situation that the rate functional of the corresponding large deviation principle admits two minimizers. We obtain different type of limits, in a positive recurrent regime, depending on the co-dimension of the subspace and the conditions imposed at the final time under the presence or absence of a wall. The motivation comes from the study of polymers or (1 + 1)-dimensional interfaces with δ-pinning.

Abstract

We study scaling limits for d-dimensional Gaussian random walks perturbed by an attractive force toward a certain subspace of $$\mathbb {R}^d$$, especially under the critical situation that the rate functional of the corresponding large deviation principle admits two minimizers. We obtain different type of limits, in a positive recurrent regime, depending on the co-dimension of the subspace and the conditions imposed at the final time under the presence or absence of a wall. The motivation comes from the study of polymers or (1 + 1)-dimensional interfaces with δ-pinning.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2009
Deposited On:11 Nov 2009 14:33
Last Modified:06 Dec 2017 21:33
Publisher:Springer
ISSN:0178-8051
Additional Information:The original publication is available at www.springerlink.com
Publisher DOI:https://doi.org/10.1007/s00440-007-0132-8
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2475669

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