Generic critical points of normal matrix ensembles
Mathematical Physics
2009-11-11 v1 Mesoscale and Nanoscale Physics
math.MP
Exactly Solvable and Integrable Systems
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 is described by the first Painlev\'e transcendent. The regularization of the curve resulting from discretization is discussed.
Keywords
Cite
@article{arxiv.math-ph/0511066,
title = {Generic critical points of normal matrix ensembles},
author = {Razvan Teodorescu},
journal= {arXiv preprint arXiv:math-ph/0511066},
year = {2009}
}
Comments
Based on a talk given at the conference on Random Matrices, Random Processes and Integrable Systems, CRM Montreal, June 2005