Titlebook: Seminar on Stochastic Analysis, Random Fields and Applications IV; Centro Stefano Frans Robert C. Dalang,Marco Dozzi,Francesco Russo Confer

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Gaussian Random Fields on Manifoldsscribes the intrinsic interest of the area,a number of possible applications and some interesting new geometric and probabilistic results. In particular,it attempts to show how the manifold approach provides a setting not only for establishing new results about Gaussian processes,but also for developing a deeper understanding of old ones.

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Higher Order Expansions for the Overlap of the SK Modelansion for the expected value of some genereral polynomial of the overlap of the system when the size . grows to infinity. Some of the coefficients obtained are shown to be vanishing, while the procedure to get the nontrivial ones has to be performed by a computer program, due to the great amount of computation involved.

MEET

Averaging of a Parabolic Partial Differential Equation with Random Evolutionefficients rapidly oscillating both in space and time variables. We extend to α < 2 and α > 2, the results by Pardoux and Piatnitski [.] (the case α = 2), and show that the structure of the limit problem depends crucially on α.

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Random Currents and Probabilistic Models of Vortex Filamentsollowing [.] and then we relate it to vortex filaments, in a new way with respect to [., ., .], but we also recall some facts from these works for comparison. Finally, we describe some attempts to define Gibbs measures on vortex lines. Related problems to random currents are:

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Seminar on Stochastic Analysis, Random Fields and Applications IV978-3-0348-7943-9Series ISSN 1050-6977 Series E-ISSN 2297-0428

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