The Mother Body Phase Transition in the Normal Matrix Model(English, Paperback, Bleher Pavel M.)

Know about the book -

The Mother Body Phase Transition in the Normal Matrix Model(English, Paperback, Bleher Pavel M.) is written by Bleher Pavel M. and published by American Mathematical Society. It's available with International Standard Book Number or ISBN identification 1470441845 (ISBN 10) and 9781470441845 (ISBN 13).

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 the authors consider the normal matrix model with cubic plus linear potential. In order to regularize the model, they follow Elbau & Felder and introduce a cut-off. In the large size limit, the eigenvalues of the model accumulate uniformly within a certain domain $\Omega$ that they determine explicitly by finding the rational parametrization of its boundary. The authors also study in detail the mother body problem associated to $\Omega$. It turns out that the mother body measure $\mu_*$ displays a novel phase transition that we call the mother body phase transition: although $\partial \Omega$ evolves analytically, the mother body measure undergoes a ``one-cut to three-cut'' phase transition.