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OverviewThe 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. Full Product DetailsAuthor: Pavel M. Bleher , Guilherme L. F. SilvaPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.333kg ISBN: 9781470441845ISBN 10: 1470441845 Pages: 144 Publication Date: 30 March 2021 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsAuthor InformationPavel M. Bleher, Indiana University-Purdue University, Indianapolis, IN, USA. Guilherme L. F. Silva, Katholieke Universiteit Leuven, Belgium. Tab Content 6Author Website:Countries AvailableAll regions |