摘要: Studying statistical properties (e.g. certain types of concentration of measure bounds) of a dynamical system is an important problem in itself. When it comes to linear cocycles over a given base dynamics, this may also have important consequences on the regularity of the corresponding Lyapunov exponents and Oseledets subspaces (regarded as functions of the cocycle). Furthermore, as important examples of linear cocycles arise in connection with solving the eigenvalue equation of a discrete Schrodinger or Jacobi operator, these types of properties are also crucial in the spectral theory of such operators from mathematical physics. In this talk I will describe these connections and some of the techniques used to establish such statistical properties for cocycles over a torus translation and over a Bernoulli shift.