Scaling limits of a heavy tailed Markov renewal process.
Résumé
We first show the convergence of a rescaled heavy tailed Markov renewal process $(\tau,J)$ towards the $\ga$-stable regenerative set. As the state space of the governing Markov chain $J$ is continuous, one has to resort to the integrated behavior of the Markov mass renewal function. In a second part we apply this result to the critical regime of the strip wetting model. We compute the scaling limits of the contact points of the polymer with the strip by giving the explicit form of its Radon Nykodym derivative with respect to the law of the zero level set of a standard brownian motion.
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