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Scaling limit of wetting models in 1+1 dimensions pinned to a shrinking strip
Stochastic Processes and their Applications ( IF 1.4 ) Pub Date : 2019-08-01 , DOI: 10.1016/j.spa.2019.08.001
Jean-Dominique Deuschel , Tal Orenshtein

We consider wetting models in $1+1$ dimensions on a shrinking strip with a general pinning function. We show that under diffusive scaling, the interface converges in law to to the reflected Brownian motion, whenever the strip size is $o(N^{-1/2})$ and the pinning function is close enough to critical value of the so-called $\delta$-pinning model of Deuschel, Giacomin, and Zambotti [DGZ05]. As a corollary, the same result holds for the constant pinning strip wetting model at criticality with $o(N^{-1/2})$ strip size.

中文翻译:

固定在收缩条上的 1+1 维润湿模型的缩放限制

我们在具有一般钉扎功能的收缩带上考虑 $1+1$ 尺寸的润湿模型。我们表明,在扩散缩放下,当条带大小为 $o(N^{-1/2})$ 并且钉扎函数足够接近 so 的临界值时,界面在法律上收敛到反射的布朗运动-称为 Deuschel、Giacomin 和 Zambotti 的 $\delta$-pinning 模型 [DGZ05]。作为推论,相同的结果适用于具有 $o(N^{-1/2})$ 条带尺寸的临界状态下的恒定钉扎条带润湿模型。
更新日期:2019-08-01
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