Lecture Series in Probability Theory

mathematical physics probability

Audience: Researchers in the topic
Seminar series times: No fixed schedule
Organizer: Insuk Seo*
*contact for this listing

The theory of hydrodynamic limits of interacting particle systems is a well developed subject in statistical mechanics. These hydrodynamic limits aim to derive solutions of PDEs as scaling limits of observables of stochastic systems such as density, energy, momentum, etc.. One can understand these scaling limits as law of large numbers on a functional space. Therefore, the corresponding CLT appears as a natural question. Surprisingly, a general approach to derive these CLTs is only available in equilibrium, namely in situations in which the underlying system is in a stationary state. The aim of this minicourse is to describe a novel approach that allows to derive such CLTs for a large class of systems and initial states. The corresponding limit turns out to be a stochastic heat equation with space-and-time-inhomogeneous noise. In order to reduce technical problems to a minimum, we will discuss in detail one particular example, the so-called reaction-diffusion model, starting from translation-invariant initial states. (Zoom address: snu-ac-kr.zoom.us/my/snuinsukseo )

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