Scaling limits of a heavy tailed Markov renewal process

Abstract

In this paper we consider heavy tailed Markov renewal processes and we prove that, suitably renormalised, they converge in law towards the $\ga$-stable regenerative set. We then apply these results to the strip wetting model which is a random walk $S$ constrained above a wall and rewarded or penalized when it hits the strip $[0,\infty )\times [0,a]$ where $a$ is a given positive number. The convergence result that we establish allows to characterize the scaling limit of this process at criticality.

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Cited by in corpus (3)

• The scaling limits of the non critical strip wetting model
• Localization of a one-dimensional simple random walk among power-law renewal obstacles
• Multi-level pinning problems for random walks and self-avoiding lattice paths