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Asymptotics of Random Matrices and Related Models: The Uses of Dyson-Schwinger Equations, Alice Guionnet


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Автор: Alice Guionnet
Название:  Asymptotics of Random Matrices and Related Models: The Uses of Dyson-Schwinger Equations
ISBN: 9781470450274
Издательство: Mare Nostrum (Eurospan)
Классификация:

ISBN-10: 1470450275
Обложка/Формат: Paperback
Страницы: 144
Вес: 0.28 кг.
Дата издания: 30.04.2019
Серия: Cbms regional conference series in mathematics
Язык: English
Размер: 181 x 256 x 15
Читательская аудитория: Professional and scholarly
Ключевые слова: Mathematical physics
Подзаголовок: The uses of dyson-schwinger equations
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Поставляется из: Англии
Описание: Probability theory is based on the notion of independence. The celebrated law of large numbers and the central limit theorem describe the asymptotics of the sum of independent variables. However, there are many models of strongly correlated random variables: for instance, the eigenvalues of random matrices or the tiles in random tilings. Classical tools of probability theory are useless to study such models.These lecture notes describe a general strategy to study the fluctuations of strongly interacting random variables. This strategy is based on the asymptotic analysis of Dyson-Schwinger (or loop) equations: the author will show how these equations are derived, how to obtain the concentration of measure estimates required to study these equations asymptotically, and how to deduce from this analysis the global fluctuations of the model. The author will apply this strategy in different settings: eigenvalues of random matrices, matrix models with one or several cuts, random tilings, and several matrices models.
Дополнительное описание: Mathematical physics


Asymptotics of Linear Differential Equations

Автор: M.H. Lantsman
Название: Asymptotics of Linear Differential Equations
ISBN: 0792371933 ISBN-13(EAN): 9780792371939
Издательство: Springer
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Цена: 102480.00 T
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Описание: Devoted to the asymptotic theory of differential equations, this book considers problems based on the notion of an asymptotic space. It contains the theoretical material and general methods of its application to partial problems, and results of asymptotic behavior of functions, integrals, and solutions of differential and difference equations.

Asymptotics of Nonlinearities and Operator Equations

Автор: M. Martin; Alexander Krasnoselskii
Название: Asymptotics of Nonlinearities and Operator Equations
ISBN: 3034898991 ISBN-13(EAN): 9783034898997
Издательство: Springer
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Цена: 97820.00 T
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Описание: New methods for solving classical problems in the theory of nonlinear operator equations (solvability, multiple solutions, bifurcations, nonlinear resonance, potential methods, etc) are introduced and discussed. In particular, the problem on forced periodic oscillations is considered for equations arising in control theory.

Asymptotics of Analytic Difference Equations

Автор: G. K. Immink
Название: Asymptotics of Analytic Difference Equations
ISBN: 3540138676 ISBN-13(EAN): 9783540138679
Издательство: Springer
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Цена: 23250.00 T
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Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations

Автор: P.L. Sachdev; Ch. Srinivasa Rao
Название: Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations
ISBN: 1461424909 ISBN-13(EAN): 9781461424901
Издательство: Springer
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Цена: 93160.00 T
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Описание: The goals of this text are to prove or disprove the solution of reduced nonlinear ODE`s by different analytic methods, and to show that these solutions are intermediate asymptotics of a class of initial/boundary conditions arising from physical considerations.

Introduction to random matrices

Автор: Anderson, Greg W. Guionnet, Alice Zeitouni, Ofer
Название: Introduction to random matrices
ISBN: 0521194520 ISBN-13(EAN): 9780521194525
Издательство: Cambridge Academ
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Цена: 73920.00 T
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Описание: The theory of random matrices plays an important role in many areas of pure mathematics. This rigorous introduction is specifically designed for graduate students in mathematics or related sciences, who have a background in probability theory but have not been exposed to advanced notions of functional analysis, algebra or geometry.

Asymptotics beyond All Orders

Автор: Harvey Segur; Saleh Tanveer; Herbert J. Levine
Название: Asymptotics beyond All Orders
ISBN: 1475704372 ISBN-13(EAN): 9781475704372
Издательство: Springer
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Цена: 95770.00 T
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Описание: Proceedings of a NATO ARW held in La Jolla, California, January 7-11, 1991

Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations

Автор: Johannes Sj?strand
Название: Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations
ISBN: 303010818X ISBN-13(EAN): 9783030108182
Издательство: Springer
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Цена: 102480.00 T
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Описание: The asymptotic distribution of eigenvalues of self-adjoint differential operators in the high-energy limit, or the semi-classical limit, is a classical subject going back to H. Weyl of more than a century ago.In the last decades there has been a renewed interest in non-self-adjoint differential operators which have many subtle properties such as instability under small perturbations. Quite remarkably, when adding small random perturbations to such operators, the eigenvalues tend to distribute according to Weyl's law (quite differently from the distribution for the unperturbed operators in analytic cases). A first result in this direction was obtained by M. Hager in her thesis of 2005. Since then, further general results have been obtained, which are the main subject of the present book.Additional themes from the theory of non-self-adjoint operators are also treated. The methods are very much based on microlocal analysis and especially on pseudodifferential operators. The reader will find a broad field with plenty of open problems.

Microlocal Analysis, Sharp Spectral Asymptotics and Applications III

Автор: Victor Ivrii
Название: Microlocal Analysis, Sharp Spectral Asymptotics and Applications III
ISBN: 3030305368 ISBN-13(EAN): 9783030305369
Издательство: Springer
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Цена: 130430.00 T
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Описание: The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schr?dinger operator, miscellaneous problems, and multiparticle quantum theory.In this volume the methods developed in Volumes I and II are applied to the Schr?dinger and Dirac operators in smooth settings in dimensions 2 and 3.

Half-century Of Physical Asymptotics And Other Diversions, A: Selected Works By Michael Berry

Автор: Berry Michael Victor
Название: Half-century Of Physical Asymptotics And Other Diversions, A: Selected Works By Michael Berry
ISBN: 9813221208 ISBN-13(EAN): 9789813221208
Издательство: World Scientific Publishing
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Цена: 65470.00 T
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Описание: 'Comments made on the philosophy and conduct of science are valuable and have been influenced strongly by academic contacts at the University of Bristol, and indeed worldwide ... The variety of papers and their intended readerships make much of this volume appropriate and enjoyable for general readers, as well as for specialists.'Contemporary PhysicsMichael Berry is a theoretical physicist who has contributed to a wide variety of areas in quantum mechanics, optics and related mathematics, linked by the geometrical aspects of waves, especially phase. This collection of his selected published and unpublished papers, reviews, tributes to other scientists, speeches and other works ranges from the technical to the popular. It is organized by the themes of his significant scientific contributions. Detailed introductions emphasize the rich connections between the different themes. An essential read for physicists, mathematicians, students and philosophers of science.

Microlocal Analysis, Sharp Spectral Asymptotics and Applications V

Автор: Victor Ivrii
Название: Microlocal Analysis, Sharp Spectral Asymptotics and Applications V
ISBN: 3030305600 ISBN-13(EAN): 9783030305604
Издательство: Springer
Рейтинг:
Цена: 130430.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schr?dinger operator, miscellaneous problems, and multiparticle quantum theory.In this volume the methods developed in Volumes I, II, III and IV are applied to multiparticle quantum theory (asymptotics of the ground state energy and related problems), and to miscellaneous spectral problems.

Microlocal Analysis, Sharp Spectral Asymptotics and Applications I

Автор: Victor Ivrii
Название: Microlocal Analysis, Sharp Spectral Asymptotics and Applications I
ISBN: 3030305562 ISBN-13(EAN): 9783030305567
Издательство: Springer
Рейтинг:
Цена: 130430.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schr?dinger operator, miscellaneous problems, and multiparticle quantum theory.In this volume the general microlocal semiclassical approach is developed, and microlocal and local semiclassical spectral asymptotics are derived.

Symbolic Asymptotics

Автор: John R. Shackell
Название: Symbolic Asymptotics
ISBN: 3642059252 ISBN-13(EAN): 9783642059254
Издательство: Springer
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Цена: 130430.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Accessible to anyone with a good general background in mathematics, but it nonetheless gets right to the cutting edge of active research. Some results appear here for the first time, while others have hitherto only been given in preprints.


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