Rhiannon Dougall

Counting Limit Theorems for Anosov Representations

We study the statistics of matrix products along geodesics in word hyperbolic groups. Specifically we assume that ρ is a dominated representation in GL(d, R). these are also called Anosov representations and are considered a generalization of convex cocompact in higher rank. We count group elements according to their word length for which singular values of matrices ρ(γ) have some prescribed growth in the word length |γ|. For these counting problems we obtain results of the genre: unique maximum, local large deviations, and a central limit theorem. This is joint work with S Cantrell, I Cipriano, C Sert.