Seminario di Probabilità e Finanza Matematica: Polynomial chaos and scaling limits of disordered systems

Venerdì 11 Ottobre 2013, ore 15:00 - Aula 2BC60 - Francesco Caravenna


Seminario di Probabilità e Finanza Matematica

Venerdì 11 Ottobre alle ore 15:00 in aula 2BC60 Il Prof. Francesco Caravenna terrà un seminario intitolato: "Polynomial chaos and scaling limits of disordered systems"

We formulate general conditions ensuring that a sequence of multi-linear polynomials of independent random variables (called polynomial chaos expansions) converges to a limiting random variable, given by an explicit Wiener chaos expansion over the d-dimensional white noise. A key ingredient is a Lindeberg-type principle for polynomial chaos.
We apply this general convergence result to study the continuum and weak disorder limits of various disordered systems that are so-called disorder relevant, which include the disordered pinning model, the directed polymer model in dimension (1+1), and the two-dimensional random field Ising model. This gives a new perspective in the study of disorder relevance, and leads to interesting new continuum models that warrant further studies.
(Joint work with Nikos Zygouras and Rongfeng Sun)