Mathematical Sciences: Theory of Random Media

随机介质理论的核心问题与近十年来在物理和数学文献中流行的局部化和间歇化思想有关。晶格局部化理论的最新进展使连续模型在物理上更加真实，特别是随机域、流形等的谱问题，以及电磁波的局部化问题。另一个问题是湍流中磁场的渐近行为，即具有随机和非线性项的麦克斯韦方程的解。随机介质理论是概率论的一个新分支，与现代数学和理论物理密切相关。这一领域的基本问题来自自然科学：无序固体物理学（包括半导体理论）、天体物理学（特别是太阳磁层和太阳风理论）和地球物理学（主要是岩石圈块体中的地震波理论）。

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.