Random matrices and Laplacian growth
The Oxford Handbook of Random Matrix Theory(2009)
摘要
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.
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关键词
eigenvalues,random matrices,two dimensions,potential theory,boundary value problem
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