The scaling limits of the non critical strip wetting model

Abstract

The strip wetting model is defined by giving a (continuous space) one dimensionnal random walk $S$ a reward $\gb$ each time it hits the strip ${\mathbb{R}}^{+}\times [0,a]$ (where $a$ is a positive parameter), which plays the role of a defect line. We show that this model exhibits a phase transition between a delocalized regime ($\gb < \gb_{c}^{a}$) and a localized one ($\gb > \gb_{c}^{a}$), where the critical point $\gb_{c}^{a} > 0$ depends on $S$ and on $a$. In this paper we give a precise pathwise description of the transition, extracting the full scaling limits of the model. Our approach is based on Markov renewal theory.

32 pages. To appear in "Stochastic Processes and their Applications"

References in corpus (2)

• Pinning and wetting transition for (1+1)-dimensional fields with Laplacian interaction
• Scaling limits of $(1+1)$-dimensional pinning models with Laplacian interaction