Breadcrumb
Self-similar measures and random walks
Thu 14 February 2013, 15:00
Peter Varju
University of Cambridge
Ergodic Theory and Dynamical Systems
Organisers: Andrew Ferguson, Thomas Jordan
ABSTRACT
I will talk about two problems. I prove that selfsimilar measures in
dimension 3 and above are absolutely continuous and have differentiable
densities, under some assumption on the rotation parts of the
selfsimilarities, if the contraction factors are sufficiently close to 1.
I will also prove a local limit theorem on exponentially small scales
for the random walk on the isometry group of Euclidean space.
Both of these results will be deduced from spectral gap estimates
on certain operators. Joint work with Elon Lindenstrauss.