Open Access
2016 Sample path large deviations for Laplacian models in $(1+1)$-dimensions
Stefan Adams, Alexander Kister, Hendrik Weber
Electron. J. Probab. 21: 1-36 (2016). DOI: 10.1214/16-EJP8


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].


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Stefan Adams. Alexander Kister. Hendrik Weber. "Sample path large deviations for Laplacian models in $(1+1)$-dimensions." Electron. J. Probab. 21 1 - 36, 2016.


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

zbMATH: 1354.60024
MathSciNet: MR3563890
Digital Object Identifier: 10.1214/16-EJP8

Primary: 60K35
Secondary: 60F10 , 82B41

Keywords: bi-harmonic , Integrated random walk , Laplacian models , large deviation , Pinning , scaling limits

Vol.21 • 2016
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