15:45
Long Range Exclusion Process
Abstract
Given a countable set of sites S an a transition matrix p(x,y) on that set, we consider a process of particles evolving on S according to the following rule: each particle waits an exponential time and then jumps following a Markov chain governed by p(x,y); the particle keeps jumping until it reaches an empty site where it remains for another exponential time. Unlike most interacting particle systems, this process fails to
have the Feller property. This causes several technical difficulties to study it. We present a method to prove that certain measures are invariant for the process and exploit the Kolmogorov zero or one law to study some of its unusual path properties.
14:15
Degenerate periodic homogenization
Abstract
The probabilistic approach to homogenization can be adapted to fully
degenerate situations, where irreducibility is insured from a Doeblin type
condition. Using recent results on weak sense Poisson equations in a
similar framework, obtained jointly with A. Veretennikov, together with a
regularization procedure, we prove the homogenization result. A similar
approach can also handle degenerate random homogenization.