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.
Deuschel, J., Orenshtein, T. (2020). Scaling limit of wetting models in 1+1 dimensions pinned to a shrinking strip. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 130(5), 2778-2807 [10.1016/j.spa.2019.08.001].
Scaling limit of wetting models in 1+1 dimensions pinned to a shrinking strip
Orenshtein T.
2020
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.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
