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Plenary lectureEntropy Expansions in Probability |
Friedrich Götze, Bielefeld University, Germany
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We investigate the convergence of sums of random variables to
Gaussian and stable laws in Entropy resp. Fischer-Information
distances. In particular we show asymptotic expansions of such
distances in terms of semi-invariants (under minimal assumptions) in
the context of classical and free probability. The results are
based on techniques of harmonic and complex analysis for the
approximation of classical and free convolutions of densities. The
common structure of asymptotic expansions for these and other limit
theorems may be explained by a scheme of approximations for
sequences of classes of symmetric functions on spaces of increasing
dimension. This is joint work with S. Bobkov, C. Chistyakov and
A. Reshetenko.
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