Colloquium, "Products of Random Matrices: Universality and Applications", Gernot Akemann, Bielefeld University
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Random matrices continue to be a popular topic among mathematicians and physicists. After introducing the concept of an ensemble of a single random matrix and its universal predictions I will review some recent progress on products of random matrices. They may serve as an example of a toy model for chaotic dynamical systems, where the Lyapunov exponents that characterize its stability can be explicitly calculated. In a particular limit of large matrix size and a large number of factors point processes are found that interpolate between the known universal statistics of a single random matrix and a deterministic Lyapunov spectrum. The interpolating kernels can be identified with that of Dyson’s Brownian Motion with fixed initial conditions.
This is joint work with Z. Burda and M. Kieburg.