New Applications of Non-Hermitian Random Matrices

Abstract

We discuss recently discovered links of the statistical models of normal random matrices to some important physical problems of pattern formation and to the quantum Hall effect. Specifically, the large N limit of the normal matrix model with a general statistical weight describes dynamics of the interface between two incompressible fluids with different viscosities in a thin plane cell (the Saffman-Taylor problem). The latter appears to be mathematically equivalent to the growth of semiclassical 2D electronic droplets in a strong uniform magnetic field with localized magnetic impurities (fluxes), as the number of electrons increases. The equivalence is most easily seen by relating both problems to the matrix model.