Generic critical points of normal matrix ensembles
Razvan Teodorescu
Abstract
The evolution of the degenerate complex curve associated with the ensemble at a generic critical point is related to the finite time singularities of Laplacian Growth. It is shown that the scaling behavior at a critical point of singular geometry x3 y2 is described by the first Painlevé transcendent. The regularization of the curve resulting from discretization is discussed.
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