Measure concentration and information distances (A04)

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In this project we shall investigate concentration of measure and large deviation tail bounds for Lipschitz type functions of high dimensional vectors of observations for various distribution classes. The large deviation behavior of functions on Euclidean spaces and on metric spaces and graphs is studied by means of gradients respectively finite differences. Furthermore, we shall investigate the convergence in the central limit theorem for sums of independent random elements in classical, non commutative and related probability theories in terms of appropriate information distances.