  The theory of random matrices with eigenvalues distributed in the complex
plane and more general "beta-ensembles" (logarithmic gases in 2D) is reviewed.
The distribution and correlations of the eigenvalues are investigated in the
large N limit. It is shown that in this limit the model is mathematically
equivalent to a class of diffusion-controlled growth models for viscous flows
in the Hele-Shaw cell and other growth processes of Laplacian type. The
analytical methods used involve the technique of boundary value problems in two
dimensions and elements of the potential theory.
