Electronic Journal of Probability

Sample path large deviations for Laplacian models in $(1+1)$-dimensions

Stefan Adams, Alexander Kister, and Hendrik Weber

Full-text: Open access

Abstract

We study scaling limits of a Laplacian pinning model in $(1+1)$ dimension and derive sample path large deviations for the profile height function. The model is given by a Gaussian integrated random walk (or a Gaussian integrated random walk bridge) perturbed by an attractive force towards the zero-level. We study in detail the behaviour of the rate function and show that it can admit up to five minimisers depending on the choices of pinning strength and boundary conditions. This study complements corresponding large deviation results for Gaussian gradient systems with pinning in $ (1+1) $-dimension ([FS04]) in $(1+d) $-dimension ([BFO09]), and recently in higher dimensions in [BCF14].

Article information

Source
Electron. J. Probab., Volume 21 (2016), paper no. 62, 36 pp.

Dates
Received: 5 February 2016
Accepted: 3 October 2016
First available in Project Euclid: 17 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1476706887

Digital Object Identifier
doi:10.1214/16-EJP8

Mathematical Reviews number (MathSciNet)
MR3563890

Zentralblatt MATH identifier
1354.60024

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60F10: Large deviations 82B41: Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41]

Keywords
Large deviation Laplacian models pinning integrated random walk scaling limits bi-harmonic

Rights
Creative Commons Attribution 4.0 International License.

Citation

Adams, Stefan; Kister, Alexander; Weber, Hendrik. Sample path large deviations for Laplacian models in $(1+1)$-dimensions. Electron. J. Probab. 21 (2016), paper no. 62, 36 pp. doi:10.1214/16-EJP8. https://projecteuclid.org/euclid.ejp/1476706887


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