## Electronic Journal of Probability

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

#### 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
Accepted: 3 October 2016
First available in Project Euclid: 17 October 2016

https://projecteuclid.org/euclid.ejp/1476706887

Digital Object Identifier
doi:10.1214/16-EJP8

Mathematical Reviews number (MathSciNet)
MR3563890

Zentralblatt MATH identifier
1354.60024

#### 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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