Applications of Random Matrix Theory in biophysics (in collaboration with Department of Theory of Complex Systems, M. Smoluchowski Institute of Physics, Jagellonian University)

Applications of random matrix theory (RMT) in physics range from interpretation of complex spectra of energy levels in atomic and nuclear physics, studies of disordered systems, chaotic behaviour to quantum gravity. Use of progressively developed methods of RMT has also proved to be of particular interest in other sciences such as meteorology, image processing, population ecology or economy.

RMT formalism can be used in various branches of physics and interdisciplinary applications where system dynamics is described in terms of evolution operators with random coefficients. One of examples is application of infinite products of random matrices to the analysis of chaotic dynamical systems, where stability of trajectories and their sensitive dependence on initial conditions are measured in terms of characteristic Lyapunov exponents. There are several results exploring the use of the formalism in studies of stability of large eco- and social-systems.

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