# 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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