February 6, 2015
Location: Janskerkhof 15a (Utrecht), room 101
Polynomial chaos and scaling limits of disordered systems I
Inspired by recent work of Alberts, Khanin and Quastel, 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 in our approach is a Lindeberg principle for polynomial chaos expansions, which extends earlier work of Mossel, O'Donnell and Oleszkiewicz. These results provide a unified framework to study the continuum and weak disorder scaling limits of statistical mechanics systems that are disorder relevant, including the disordered pinning model, the long-range 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.
This is based on joint work with F. Caravenna and N. Zygouras.
The slides of this lecture are available via this link.
Free energy fluctuations in some directed polymers and KPZ universality class
In the first part of my lecture I will discuss the KPZ universality class and present some recent results in terms of free energy fluctuations. These are the first proven results of the appearance of the Tracy–Widom distribution function for models of directed polymers at positive temperature. In the second, more technical, part of the lecture I will explain in some details how we obtained the results.