Speaker: Robert Hough
Abstract:
I will describe results of three recent papers from random walk on unipotent groups.
In joint work with Diaconis (Stanford), we obtain a new local limit theorem on the real Heisenberg group, and determine the mixing time of coordinates for some random walks on finite unipotent groups.
In a separate investigation I obtain worst case and typical mixing behavior for random walks on the cycle, proving the conjecture that the mixing time is bounded by degree times diameter squared of the corresponding Cayley graph.
In joint work with Jerison and Levine (Cornell) we prove a cut-off phenomenon in sandpile dynamics on the torus (\mathbb{Z}/m\mathbb{Z})^2 and obtain a new upper bound on the critical exponent of sandpiles on $\mathbb{Z}^2$.