We consider wetting models in 1+1 dimensions with a general pinning function on a shrinking strip. We show that under a diffusive scaling, the interface converges in law to the reflected Brownian motion, whenever the strip size is o(N−1∕2) and the pinning function is close enough to the critical value of the so-called δ-pinning model of Deuschel–Giacomin–Zambotti [10]. As a corollary, the same result holds for the constant pinning strip wetting model at criticality with order o(N−1∕2) shrinking strip.

Deuschel, J., & Orenshtein, T. (2020). Scaling limit of wetting models in 1+1 dimensions pinned to a shrinking strip. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 130(5), 2778-2807 [10.1016/j.spa.2019.08.001].

Scaling limit of wetting models in 1+1 dimensions pinned to a shrinking strip

Orenshtein T.
2020

Abstract

We consider wetting models in 1+1 dimensions with a general pinning function on a shrinking strip. We show that under a diffusive scaling, the interface converges in law to the reflected Brownian motion, whenever the strip size is o(N−1∕2) and the pinning function is close enough to the critical value of the so-called δ-pinning model of Deuschel–Giacomin–Zambotti [10]. As a corollary, the same result holds for the constant pinning strip wetting model at criticality with order o(N−1∕2) shrinking strip.
Articolo in rivista - Articolo scientifico
Entropic repulsion; Interface model; Markov renewal process; Strip-wetting model; Zero-set; δ-pinning model;
English
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Deuschel, J., & Orenshtein, T. (2020). Scaling limit of wetting models in 1+1 dimensions pinned to a shrinking strip. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 130(5), 2778-2807 [10.1016/j.spa.2019.08.001].
Deuschel, J; Orenshtein, T
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/362282
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