Scaling limits and universality for random pinning models

par M. Francesco Caravenna

lundi 10 juin 2013, 11:00 → 12:00 Europe/Paris

I103 (LAREMA)

We consider the so-called random pinning model, which may be described as a Markov chain that receives a random reward/penalty each time it visits a given site.
When the return time distribution of the Markov chain has a polynomial tail, with exponent larger than 1/2, the model is said to be disorder-relevant, since an arbitrarily small amount of external randomness (quenched disorder) changes radically the critical properties of the model. In this regime, we show that the partition function of the model, under an appropriate weak coupling scaling limit, converges to a universal quantity, given by an explicit Wiener chaos expansion.
This quantity can be viewed as the partition function of a universal "continuum random pinning model", whose construction is part of our approach. (Joint work with Nikos Zygouras and Rongfeng Sun)