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

Jean-Dominique Deuschel and Tal Orenshtein

Stochastic Processes and their Applications, 2020, vol. 130, issue 5, 2778-2807

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.

Keywords: δ-pinning model; Strip-wetting model; Entropic repulsion; Interface model; Zero-set; Markov renewal process (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2019.08.001

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