The Mother Body Phase Transition in the Normal Matrix Model (Memoirs of the American Mathematical Society, Band 265) - Softcover

Bleher, Pavel M.; Silva, Guilherme L. F.

 
9781470441845: The Mother Body Phase Transition in the Normal Matrix Model (Memoirs of the American Mathematical Society, Band 265)
Softcover
ISBN 10: 1470441845 ISBN 13: 9781470441845
Verlag: American Mathematical Society, 2020

Inhaltsangabe

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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Über die Autorin bzw. den Autor

Pavel M. Bleher, Indiana University-Purdue University, Indianapolis, IN, USA.

Guilherme L. F. Silva, Katholieke Universiteit Leuven, Belgium.

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Verlag
American Mathematical Society
Erscheinungsdatum
2020
Sprache
Englisch
ISBN 10 
1470441845
ISBN 13 
9781470441845
Einband
Taschenbuch
Anzahl der Seiten
144
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
preigu
mail@preigu.de

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