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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Supported in part by the JSPS Grants 17654020 and (A) 18204007.
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Bolthausen, E., Funaki, T. & Otobe, T. Concentration under scaling limits for weakly pinned Gaussian random walks. Probab. Theory Relat. Fields 143, 441–480 (2009). https://doi.org/10.1007/s00440-007-0132-8
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DOI: https://doi.org/10.1007/s00440-007-0132-8