Concentration under scaling limits for weakly pinned Gaussian random walks

Erwin Bolthausen; Tadahisa Funaki; Tatsushi Otobe

doi:10.1007/s00440-007-0132-8

Concentration under scaling limits for weakly pinned Gaussian random walks

Erwin Bolthausen, Tadahisa Funaki^*, Tatsushi Otobe

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

We study scaling limits for d-dimensional Gaussian random walks perturbed by an attractive force toward a certain subspace of 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.

Original language	English
Pages (from-to)	441-480
Number of pages	40
Journal	Probability Theory and Related Fields
Volume	143
Issue number	3-4
DOIs	https://doi.org/10.1007/s00440-007-0132-8
Publication status	Published - 2009 Mar
Externally published	Yes

Keywords

Concentration
Large deviation
Minimizers
Pinning
Random walks
Scaling limit

ASJC Scopus subject areas

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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10.1007/s00440-007-0132-8

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title = "Concentration under scaling limits for weakly pinned Gaussian random walks",

abstract = "We study scaling limits for d-dimensional Gaussian random walks perturbed by an attractive force toward a certain subspace of Rd, 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.",

keywords = "Concentration, Large deviation, Minimizers, Pinning, Random walks, Scaling limit",

author = "Erwin Bolthausen and Tadahisa Funaki and Tatsushi Otobe",

note = "Funding Information: Supported in part by the JSPS Grants 17654020 and (A) 18204007.",

year = "2009",

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doi = "10.1007/s00440-007-0132-8",

language = "English",

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T1 - Concentration under scaling limits for weakly pinned Gaussian random walks

AU - Bolthausen, Erwin

AU - Funaki, Tadahisa

AU - Otobe, Tatsushi

N1 - Funding Information: Supported in part by the JSPS Grants 17654020 and (A) 18204007.

PY - 2009/3

Y1 - 2009/3

N2 - We study scaling limits for d-dimensional Gaussian random walks perturbed by an attractive force toward a certain subspace of Rd, 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.

AB - We study scaling limits for d-dimensional Gaussian random walks perturbed by an attractive force toward a certain subspace of Rd, 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.

KW - Concentration

KW - Large deviation

KW - Minimizers

KW - Pinning

KW - Random walks

KW - Scaling limit

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DO - 10.1007/s00440-007-0132-8

M3 - Article

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VL - 143

SP - 441

EP - 480

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 3-4

ER -

Concentration under scaling limits for weakly pinned Gaussian random walks

Abstract

Keywords

ASJC Scopus subject areas

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