Scaling limits of disordered systems

par Nikos Zygouras

jeudi 10 nov. 2016, 14:30 → 15:30 Europe/Paris

salle 435 (UMPA)

We consider statistical mechanics models defined on a lattice, such as pinning models, directed polymers, random field Ising model, in which disorder acts as an external random field. Such models are called disorder relevant, if arbitrarily weak disorder changes the qualitative properties of the model. Via a Lindeberg principle for multilinear polynomials we show that disorder relevance manifests itself through the existence of a disordered high-temperature limit for the partition function, which is given in terms of Wiener chaos and is model specific. When disorder becomes marginally relevant a fundamentally new structure emerges, which leads to universal phenomena across all different (currently of directed polymer type) models that fall in this class, including also the two dimensional stochastic heat equation with multiplicative space-time white noise. Based on joint works with Francesco Caravenna and Rongfeng Sun.