Interacting Stochastic Systems -

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Résumé :
1 2 Jean-Dominique Deuschel and Andreas Greven 1 Fakult? at II - Mathematik und Naturwissenschaften, Institut fur ? Mathematik, Technische Universit? at Berlin, Stra?e des 17. Juni 136, D-10623 Berlin Tel. (0049 30) 314-25193, Fax: (0049 30) 314-21695 deuschel@math. tu-berlin. de 2 1 Mathematisches Institut, Bismarckstr. 1 , D-91054 Erlangen, 2 Tel. (0049 9131) 85-22454, Fax (0049 9131) 85-26214 This volume collects original work and reviews on work in the ?eld of pro- bilitywhichtookplacewithintheframeworkoftheDFG-Schwerpunkt:Int- acting stochastic systems of high complexity. This research network started in May 1997 and was funded till May 2003. In this network between 20-30 (depending on the 2-year periods of grant renewal) groups from probab- ity, statistical physics and mathematical statistics within Germany were - tive. An extensive international collaboration was an essential part of this network and here particularly intense contacts were built up between the DFG-Schwerpunkt and EURANDOM, a European institute for research in stochastics, which was founded in 1997. This partnership reached from joint workshops and colloquia to collaborations on speci?c projects. The key scienti?c idea which was behind the research network was to - plore and develop the connections between research in in?nite dimensional stochastic analysis, statistical physics (Gibbs measures, random media), s- tial population models from mathematical biology, complex models of ?n- cial markets or of stochastic models with interacting components in other sciences as for example in climatology.

Sommaire:
Stochastic Methods in Statistical Physics.- Coarse-Graining Techniques for (Random) Kac Models.- Euclidean Gibbs Measures of Quantum Crystals: Existence, Uniqueness and a Priori Estimates.- Some Jump Processes in Quantum Field Theory.- Gibbs Measures on Brownian Paths: Theory and Applications.- Spectral Theory for Nonstationary Random Potentials.- A Survey of Rigorous Results on Random Schr?dinger Operators for Amorphous Solids.- The Parabolic Anderson Model.- Random Spectral Distributions.- Stochastic in Population Models.- Renormalization and Universality for Multitype Population Models.- Stochastic Insertion-Deletion Processes and Statistical Sequence Alignment.- Branching Processes in Random Environment - A View on Critical and Subcritical Cases.- Stochastic Analysis.- Thin Points of Brownian Motion Intersection Local Times.- Coupling, Regularity and Curvature.- Two Mathematical Approaches to Stochastic Resonance.- Continuity Properties of Inertial Manifolds for Stochastic Retarded Semilinear Parabolic Equations.- The Random Walk Representation for Interacting Diffusion Processes.- Applications of Stochastic Analysis in Finance, Engineering and Algorithms.- On Worst-Case Investment with Applications in Finance and Insurance Mathematics.- Random Dynamical Systems Methods in Ship Stability: A Case Study.- Analysis of Algorithms by the Contraction Method: Additive and Max-recursive Sequences.