289990 Stochastic Analysis of Complex Networks (V) (WiSe 2008/2009)

Complex networks describe a wide range of systems in nature and society. Their analysis is by no means exhausted by probability degree statistics, but requires detailed investigations into the structural properties of a network,� finding of� measurable quantities within the network and describing their dynamical properties. We demonstrate that stochastic analysis would help much in that.
�The main intrigue of the course is the interplay between words - "graph" and "random". The first and obvious combination -- "random graphs" will be explained in details by Dr. T.Kr�ger from the Max Planck Institute for Mathematics in the Sciences (MIS, Leipzig). Then, the point of view would be somewhat alternated. Namely, the graph is considered non-random, but the "frame of reference" is now taken at random giving us a random walk on graphs. Dr. D. Volchenkow (Uni-Bielefeld) starts the course from combinatorics through the spectral graph theory to graphs as probabilistic manifolds. Herr Prof. Dr. Ph. Blanchard (Uni-Bielefeld) discusses a number of network models in biology and epidemiology. The course is interdisciplinary and can be interesting for e.g. mathematicians, physicists, bio-cybernetists, neuro-biologists,
�computer scientists and engineers. A certain background in linear algebra may be useful.