The Mother Body Phase Transition In The Normal Matrix Model
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The Mother Body Phase Transition In The Normal Matrix Model
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Author : Pavel M. Bleher
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28
The Mother Body Phase Transition In The Normal Matrix Model written by Pavel M. Bleher and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.
In this present paper, the authors consider the normal matrix model with cubic plus linear potential.
Mother Body Phase Transition In The Body Phase Transition In Normal Matrix Model
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Author : Pavel Bleher
language : en
Publisher:
Release Date : 2020
Mother Body Phase Transition In The Body Phase Transition In Normal Matrix Model written by Pavel Bleher and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Electronic books categories.
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 bo.
Progress On The Study Of The Ginibre Ensembles
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Author : Sung-Soo Byun
language : en
Publisher: Springer Nature
Release Date : 2024-08-20
Progress On The Study Of The Ginibre Ensembles written by Sung-Soo Byun and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-20 with Mathematics categories.
This open access book focuses on the Ginibre ensembles that are non-Hermitian random matrices proposed by Ginibre in 1965. Since that time, they have enjoyed prominence within random matrix theory, featuring, for example, the first book on the subject written by Mehta in 1967. Their status has been consolidated and extended over the following years, as more applications have come to light, and the theory has developed to greater depths. This book sets about detailing much of this progress. Themes covered include eigenvalue PDFs and correlation functions, fluctuation formulas, sum rules and asymptotic behaviors, normal matrix models, and applications to quantum many-body problems and quantum chaos. There is a distinction between the Ginibre ensemble with complex entries (GinUE) and those with real or quaternion entries (GinOE and GinSE, respectively). First, the eigenvalues of GinUE form a determinantal point process, while those of GinOE and GinSE have the more complicated structure of a Pfaffian point process. Eigenvalues on the real line in the case of GinOE also provide another distinction. On the other hand, the increased complexity provides new opportunities for research. This is demonstrated in our presentation, which details several applications and contains not previously published theoretical advances. The areas of application are diverse, with examples being diffusion processes and persistence in statistical physics and equilibria counting for a system of random nonlinear differential equations in the study of the stability of complex systems.
Traffic Distributions And Independence Permutation Invariant Random Matrices And The Three Notions Of Independence
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Author : Camille Male
language : en
Publisher: American Mathematical Society
Release Date : 2021-02-10
Traffic Distributions And Independence Permutation Invariant Random Matrices And The Three Notions Of Independence written by Camille Male and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-10 with Mathematics categories.
Voiculescu's notion of asymptotic free independence is known for a large class of random matrices including independent unitary invariant matrices. This notion is extended for independent random matrices invariant in law by conjugation by permutation matrices. This fact leads naturally to an extension of free probability, formalized under the notions of traffic probability. The author first establishes this construction for random matrices and then defines the traffic distribution of random matrices, which is richer than the $^*$-distribution of free probability. The knowledge of the individual traffic distributions of independent permutation invariant families of matrices is sufficient to compute the limiting distribution of the join family. Under a factorization assumption, the author calls traffic independence the asymptotic rule that plays the role of independence with respect to traffic distributions. Wigner matrices, Haar unitary matrices and uniform permutation matrices converge in traffic distributions, a fact which yields new results on the limiting $^*$-distributions of several matrices the author can construct from them. Then the author defines the abstract traffic spaces as non commutative probability spaces with more structure. She proves that at an algebraic level, traffic independence in some sense unifies the three canonical notions of tensor, free and Boolean independence. A central limiting theorem is stated in this context, interpolating between the tensor, free and Boolean central limit theorems.
Hyponormal Quantization Of Planar Domains
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Author : Björn Gustafsson
language : en
Publisher: Springer
Release Date : 2017-09-29
Hyponormal Quantization Of Planar Domains written by Björn Gustafsson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-29 with Mathematics categories.
This book exploits the classification of a class of linear bounded operators with rank-one self-commutators in terms of their spectral parameter, known as the principal function. The resulting dictionary between two dimensional planar shapes with a degree of shade and Hilbert space operators turns out to be illuminating and beneficial for both sides. An exponential transform, essentially a Riesz potential at critical exponent, is at the heart of this novel framework; its best rational approximants unveil a new class of complex orthogonal polynomials whose asymptotic distribution of zeros is thoroughly studied in the text. Connections with areas of potential theory, approximation theory in the complex domain and fluid mechanics are established. The text is addressed, with specific aims, at experts and beginners in a wide range of areas of current interest: potential theory, numerical linear algebra, operator theory, inverse problems, image and signal processing, approximation theory, mathematical physics.
Resolvent Heat Kernel And Torsion Under Degeneration To Fibered Cusps
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Author : Pierre Albin
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-21
Resolvent Heat Kernel And Torsion Under Degeneration To Fibered Cusps written by Pierre Albin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-21 with Education categories.
Manifolds with fibered cusps are a class of complete non-compact Riemannian manifolds including many examples of locally symmetric spaces of rank one. We study the spectrum of the Hodge Laplacian with coefficients in a flat bundle on a closed manifold undergoing degeneration to a manifold with fibered cusps. We obtain precise asymptotics for the resolvent, the heat kernel, and the determinant of the Laplacian. Using these asymptotics we obtain a topological description of the analytic torsion on a manifold with fibered cusps in terms of the R-torsion of the underlying manifold with boundary.
Paley Wiener Theorems For A P Adic Spherical Variety
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Author : Patrick Delorme
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-21
Paley Wiener Theorems For A P Adic Spherical Variety written by Patrick Delorme and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-21 with Education categories.
Let SpXq be the Schwartz space of compactly supported smooth functions on the p-adic points of a spherical variety X, and let C pXq be the space of Harish-Chandra Schwartz functions. Under assumptions on the spherical variety, which are satisfied when it is symmetric, we prove Paley–Wiener theorems for the two spaces, characterizing them in terms of their spectral transforms. As a corollary, we get relative analogs of the smooth and tempered Bernstein centers — rings of multipliers for SpXq and C pXq.WhenX “ a reductive group, our theorem for C pXq specializes to the well-known theorem of Harish-Chandra, and our theorem for SpXq corresponds to a first step — enough to recover the structure of the Bern-stein center — towards the well-known theorems of Bernstein [Ber] and Heiermann [Hei01].
Local Well Posedness And Break Down Criterion Of The Incompressible Euler Equations With Free Boundary
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Author : Chao Wang
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-07-21
Local Well Posedness And Break Down Criterion Of The Incompressible Euler Equations With Free Boundary written by Chao Wang and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-21 with Education categories.
In this paper, we prove the local well-posedness of the free boundary problem for the incompressible Euler equations in low regularity Sobolev spaces, in which the velocity is a Lipschitz function and the free surface belongs to C 3 2 +ε. Moreover, we also present a Beale-Kato-Majda type break-down criterion of smooth solution in terms of the mean curvature of the free surface, the gradient of the velocity and Taylor sign condition.
Gromov Witten Theory Of Quotients Of Fermat Calabi Yau Varieties
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Author : Hiroshi Iritani
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-21
Gromov Witten Theory Of Quotients Of Fermat Calabi Yau Varieties written by Hiroshi Iritani and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-21 with Education categories.
Gromov-Witten theory started as an attempt to provide a rigorous mathematical foundation for the so-called A-model topological string theory of Calabi-Yau varieties. Even though it can be defined for all the Kähler/symplectic manifolds, the theory on Calabi-Yau varieties remains the most difficult one. In fact, a great deal of techniques were developed for non-Calabi-Yau varieties during the last twenty years. These techniques have only limited bearing on the Calabi-Yau cases. In a certain sense, Calabi-Yau cases are very special too. There are two outstanding problems for the Gromov-Witten theory of Calabi-Yau varieties and they are the focus of our investigation.
Differential Function Spectra The Differential Becker Gottlieb Transfer And Applications To Differential Algebraic K Theory
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Author : Ulrich Bunke
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-21
Differential Function Spectra The Differential Becker Gottlieb Transfer And Applications To Differential Algebraic K Theory written by Ulrich Bunke and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-21 with Education categories.
We develop differential algebraic K-theory for rings of integers in number fields and we construct a cycle map from geometrized bundles of modules over such a ring to the differential algebraic K-theory. We also treat some of the foundational aspects of differential cohomology, including differential function spectra and the differential Becker-Gottlieb transfer. We then state a transfer index conjecture about the equality of the Becker-Gottlieb transfer and the analytic transfer defined by Lott. In support of this conjecture, we derive some non-trivial consequences which are provable by independent means.