Mathematical Sciences: Theory of Random Media

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The central problems in the random media theory are connected with the ideas of localization and intermittency which were popular in the physical and mathematical literature during last decade. Recent progress in the lattice localization theory makes the continuous models more realistic physically, especially spectral problems for the random domains, manifolds, etc., and localization for the electromagnetic waves. Another issue is the asymptotic behavior of magnetic fields in turbulent flows, i.e. the solutions of the Maxwell equations with random and non-linear terms. This set of problems is important in astrophysical applications (non-linear solar dynamo,solar wind etc.) Random media theory is a new branch of probability theory closely connected with the modern mathematical and theoretical physics. The basic problems on this area come from the natural sciences: disordered solid state physics(including the theory of semiconductors), astrophysics,in particular the theory of solar magnetosphere and solar wind, and geophysics, mainly the theory of seismic waves in lithosphere blocks with cracks.