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

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  • Deuschel, Jean-Dominique
  • Orenshtein, Tal

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.

Suggested Citation

  • Deuschel, Jean-Dominique & Orenshtein, Tal, 2020. "Scaling limit of wetting models in 1+1 dimensions pinned to a shrinking strip," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 2778-2807.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:5:p:2778-2807
    DOI: 10.1016/j.spa.2019.08.001
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    References listed on IDEAS

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    1. Sohier, Julien, 2015. "The scaling limits of the non critical strip wetting model," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3075-3103.
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