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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Deuschel, Jean-Dominique¹  Orenshtein, Tal^1,2 

[1] Tech Univ Berlin, Str 17 Juni 135, D-10623 Berlin, Germany

[2] Humboldt Univ, Unter Linden 6, D-10117 Berlin, Germany

关键词: delta-pinning model;    Strip-wetting model;    Entropic repulsion;    Interface model;    Zero-set;    Markov renewal process;   

DOI  :  10.1016/j.spa.2019.08.001

来源: Elsevier

【 摘 要 】

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 6-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. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

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