Scaling limit of wetting models in $1+1$ dimensions pinned to a shrinking strip
| Autor: | Deuschel, Jean-Dominique, Orenshtein, Tal |
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| Rok vydání: | 2018 |
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| Zdroj: | Stochastic Processes and their Applications, Elsevier, vol. 130(5), 2020, pages 2778-2807 |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 29 pages, 1 figure |
| Databáze: | arXiv |
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