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The Mother Body Phase Transition in the Normal Matrix Model.
・ISBN 978-1-4704-4184-5 paper US$ 85.00
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| 著者・編者 | Bleher, Pavel M. / Silva, Guilherme L. F., |
|---|---|
| シリーズ | (Memoirs of the American Mathematical Society) |
| 出版社 | (American Mathematical Society, US) |
| 出版年月 | 2021 |
| ページ数 | 144 pp. |
| 言語 | ENG |
| ニュース番号 | ＜A02-21712＞ |
解説
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.
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.