The scaling limits of a heavy tailed Markov renewal process.(English. French summary)Zbl 1271.60095

Author’s abstract: In this paper we consider heavy tailed Markov renewal processes and we prove that, suitably renormalised, they converge in law towards the $$\alpha$$-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.

MSC:

 60K15 Markov renewal processes, semi-Markov processes 60K05 Renewal theory 60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.) 82B27 Critical phenomena in equilibrium statistical mechanics
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