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The Mother Body Phase Transition in the Normal Matrix Model

2020-09-28 Mathematics
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Release : 2020-09-28
Genre : Mathematics
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Book Rating : 845/5 ( reviews)

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Book Synopsis The Mother Body Phase Transition in the Normal Matrix Model by : Pavel M. Bleher

Download or read book The Mother Body Phase Transition in the Normal Matrix Model written by Pavel M. Bleher. This book was released on 2020-09-28. Available in PDF, EPUB and Kindle. Book excerpt: In this present paper, the authors consider the normal matrix model with cubic plus linear potential.

Progress on the Study of the Ginibre Ensembles

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Book Synopsis Progress on the Study of the Ginibre Ensembles by : Sung-Soo Byun

Download or read book Progress on the Study of the Ginibre Ensembles written by Sung-Soo Byun. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt:

Traffic Distributions and Independence: Permutation Invariant Random Matrices and the Three Notions of Independence

2021-02-10 Mathematics
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Release : 2021-02-10
Genre : Mathematics
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Book Rating : 981/5 ( reviews)

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Book Synopsis Traffic Distributions and Independence: Permutation Invariant Random Matrices and the Three Notions of Independence by : Camille Male

Download or read book Traffic Distributions and Independence: Permutation Invariant Random Matrices and the Three Notions of Independence written by Camille Male. This book was released on 2021-02-10. Available in PDF, EPUB and Kindle. Book excerpt: 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

2017-09-29 Mathematics
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Release : 2017-09-29
Genre : Mathematics
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Book Rating : 107/5 ( reviews)

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Book Synopsis Hyponormal Quantization of Planar Domains by : Björn Gustafsson

Download or read book Hyponormal Quantization of Planar Domains written by Björn Gustafsson. This book was released on 2017-09-29. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Gromov-Witten Theory of Quotients of Fermat Calabi-Yau Varieties

2021-06-21 Education
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Release : 2021-06-21
Genre : Education
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Book Rating : 635/5 ( reviews)

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Book Synopsis Gromov-Witten Theory of Quotients of Fermat Calabi-Yau Varieties by : Hiroshi Iritani

Download or read book Gromov-Witten Theory of Quotients of Fermat Calabi-Yau Varieties written by Hiroshi Iritani. This book was released on 2021-06-21. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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