EVENT DETAILS AND ABSTRACT

Title: Ergodic theory of quasi-periodic diffusions with applications to interface motions
Speaker: Peter Morfe
Speaker Info: U. Chicago
Brief Description:
Special Note:
Abstract:

I will discuss the invariant measures of a family of quasi-periodic diffusion processes parametrized by the unit sphere. The analysis of these processes is motivated by the homogenization of a certain class of interface motions in periodic media, where the invariant measures appear in the formula for the homogenized coefficients. The main question is the limiting behavior of the family of invariant measures as the sphere parameter varies. At irrational directions on the sphere, the invariant measures are continuous; but, in rational directions, the limiting behavior depends on the direction of approach. I will present a heuristic argument that provides an explicit formula for the limiting measures in the rational case.