Homogenization of random trajectories and shapes

par Marek Biskup (UCLA)

lundi 15 mai 2017, 16:15 → 17:15 Europe/Paris

Fokko du Cloux (UCBL-Braconnier)

As it turns out, many physical phenomena at our (human) scales are governed by continuum equations and/or variational problems for functionals with regularly varying coefficients. However, the assumed regularity is at odds with the fact that the ambient environment for these problems often rapidly oscillates at microscopic scales due to, for instance, the atomic nature of matter etc. This is reconciled mathematically by homogenization theory, which is a set of tools to show that these oscillations average out, or homogenize, when a proper scaling limit is taken. The underlying microscopic structure is then ultimately reflected only in the values of the above coefficients. In my talk, I will discuss a few examples of this phenomenon. Specifically, I will focus on the scaling limits of random walk trajectories and random shapes in random environments where a definite answer is possible. No technical background in this subject area will be assumed.