Electronic Journal of Probability
- Electron. J. Probab.
- Volume 21 (2016), paper no. 62, 36 pp.
Sample path large deviations for Laplacian models in $(1+1)$-dimensions
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].
Electron. J. Probab., Volume 21 (2016), paper no. 62, 36 pp.
Received: 5 February 2016
Accepted: 3 October 2016
First available in Project Euclid: 17 October 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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