# 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.

## Statistics

### Citations

7 citations in Web of Science®
6 citations in Scopus®

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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English 2009 11 Nov 2009 14:33 05 Apr 2016 13:31 Springer 0178-8051 The original publication is available at www.springerlink.com https://doi.org/10.1007/s00440-007-0132-8 http://www.ams.org/mathscinet-getitem?mr=2475669