Generic critical points of normal matrix ensembles

Details Generic critical points of normal matrix ensembles Generic critical points of normal matrix ensembles

2005-11-21

arxiv.org/abs/math-ph/0511066v1

J. Phys. A: Math. Gen. 39 (2006) 8921 - 8932

Physics

Mathematical Physics

Based on a talk given at the conference on Random Matrices, Random Processes and Integrable Systems, CRM Montreal, June 2005

Scientific paper

10.1088/0305-4470/39/28/S09

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 $x^3 \sim y^2$ is described by the first Painlev\'e transcendent. The regularization of the curve resulting from discretization is discussed.

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