Multidimensional Stochastic Models and Their Applications

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The developments of Probability, Statistics, and their applications lead to increasingly complex models, involving a large number of variables as well as hidden or explicit parameters including a variety of random factors as well. The objects of our research like random matrices and random polynomials, Gaussian fields, random polytopes, fractional Laplacians as generators of Levy processes, U-max statistics and kernel density estimators are topics which are currently intensively studied. Research in this area requires the solution of basic open questions in modern Probability and Statistics using techniques relying on the latest mathematical achievements. In particular we shall concentrate on the solution of open problems concerning U-max statistics, the relation of random polytopes and intrinsic volumes to Gaussian random matrices and Gaussian processes, complexity measures for quantization and coding errors and the distribution of fractional processes as well as problems of small deviations.