The scaling limits of the non critical strip wetting model

Julien Sohier

Stochastic Processes and their Applications, 2015, vol. 125, issue 8, 3075-3103

Abstract: The strip wetting model is defined by giving a (continuous space) one dimensional random walk S a reward β each time it hits the strip R+×[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 (β<βca) and a localized one (β>βca), where the critical point βca>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.

Keywords: Scaling limits for physical systems; Fluctuation theory for random walks; Markov renewal theory (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2015.02.012

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