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The Mother Body Phase Transition in the Normal Matrix Model
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eBook
The Mother Body Phase Transition in the Normal Matrix Model
2020
Overview
The normal matrix model with algebraic potential has gained a lot of attention recently, partially in virtue of its connection to
several other topics as quadrature domains, inverse potential problems and the Laplacian growth.
In this present paper we
consider the normal matrix model with cubic plus linear potential. In order to regularize the model, we follow Elbau & Felder and
introduce a cut-off. In the large size limit, the eigenvalues of the model accumulate uniformly within a certain domain
We also study in detail the mother body problem associated to
To construct the mother body measure, we define a quadratic differential
Following previous works of Bleher & Kuijlaars
and Kuijlaars & López, we consider multiple orthogonal polynomials associated with the normal matrix model. Applying the Deift-Zhou
nonlinear steepest descent method to the associated Riemann-Hilbert problem, we obtain strong asymptotic formulas for these polynomials.
Due to the presence of the linear term in the potential, there are no rotational symmetries in the model. This makes the construction of
the associated
Publisher
American Mathematical Society
Subject
ISBN
9781470441845, 1470441845
