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 ...
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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.
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Add this copy of The Mother Body Phase Transition in the Normal Matrix to cart. $92.35, new condition, Sold by Literary Cat Books rated 2.0 out of 5 stars, ships from Machynlleth, Powys, WALES, UNITED KINGDOM, published 2020 by American Mathematical Society.
Add this copy of The Mother Body Phase Transition in the Normal Matrix to cart. $144.71, new condition, Sold by Ria Christie Books rated 4.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2021 by American Mathematical Society.
