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.
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