Graduate Geometry, Topology and Dynamics Seminar
Mike Cantrell
UIC
Subadditive Ergodic Theorem for Finitely Generated Nilpotent Groups
Abstract: Kingmann's subadditive ergodic theorem has proved to be a powerful tool in many dynamical situations; it can be thought of as an ergodic theorem for a probability measure-preserving subadditive cocycle over the integers.
I will discuss a generalization of this to a cocycle over a finitely generated nilpotent group from the equivalent point of view of a measurable equivariant family of random metrics on the group.
Seen this way, our result is a randomized version of Pansu's theorem that f.g. nilpotent groups have a unique asymptotic cone.
We will also see applications to first passage percolation.
Wednesday April 15, 2015 at 3:00 PM in SEO 612