The Research Network on "Interacting stochastic systems of high complexity" set up by the German Research Foundation aimed at exploring and developing connections between research in infinite-dimensional stochastic analysis, statistical physics, spatial population models from mathematical biology, complex models of financial markets or of stochastic models interacting with other sciences. This book presents a structured collection of papers on the core topics, written at the close of the 6-year programme by the research groups who took part in it. The structure chosen highlights the interweaving of certain themes and certain interconnections discovered through the joint work. This yields a reference work on results and methods that will be useful to all who work between applied probability and the physical, economic, and life sciences. The Research Network on "Interacting stochastic systems of high complexity" set up by the German Research Foundation aimed at exploring and developing connections between research in infinite-dimensional stochastic analysis, statistical physics, spatial population models from mathematical biology, complex models of financial markets or of stochastic models interacting with other sciences. This book presents a structured collection of papers on the core topics, written at the close of the 6-year programme by the researchgroups who took part in it. The structure chosen highlights the interweaving of certain themes and certain interconnections discovered through the joint work. This yields a reference work on results and methods that will be useful to all who work between applied probability and the physical, economic, and life sciences. TOC:Random dynamical systems methods in ship stability: a case study, Coarse-Graining Techniques for (random) Kac Models, The random walk representation for interacting diffusion processes, The Parabolic Anderson Model, Some Jump Processes in Quantum Field Theory, Random matrices, random permutations and statistics of zeta zero, Renormalization and universality for multitype population models, Two Mathematical Approaches to Stochastic Resonance, Branching Processes in random environment - a view on critical and subcritical cases, Spectral theory for nonstationary random potentials, Thin points of Brownian motion intersection local times, On worst-case investment with applications in finance and insurance mathematics, A survey of rigorous results on random Schrödinger operators for amorphous solids, Analysis of a Markov chain algorithm on spanning trees by multicommodity flows, Continuity Properties of Inertial Manifolds for Stochastic Retarded Semilinear Parabolic Equations, Coupling, Regularity and Curvature, Stochastic insertion-deletion processes and statistical sequence alignment, Gibbs measures on Brownian paths: Theory and Applications Mean field theory is one of the standard tools of statistical mechanics to get a fast first insight into the behaviour of a complex interacting system. Core papers emanating from the research network, DFG-Schwerpunkt: Interacting stochastic systems of high complexity
