theory-of-random-determinants

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Theory Of Random Determinants

Author : V.L. Girko
ISBN : 9789400918580
Genre : Mathematics
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'Et mm. ..., si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point all':'' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf IIClI.t to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Random Matrices

Author : Madan Lal Mehta
ISBN : 008047411X
Genre : Mathematics
File Size : 29. 23 MB
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Random Matrices gives a coherent and detailed description of analytical methods devised to study random matrices. These methods are critical to the understanding of various fields in in mathematics and mathematical physics, such as nuclear excitations, ultrasonic resonances of structural materials, chaotic systems, the zeros of the Riemann and other zeta functions. More generally they apply to the characteristic energies of any sufficiently complicated system and which have found, since the publication of the second edition, many new applications in active research areas such as quantum gravity, traffic and communications networks or stock movement in the financial markets. This revised and enlarged third edition reflects the latest developements in the field and convey a greater experience with results previously formulated. For example, the theory of skew-orthogoanl and bi-orthogonal polynomials, parallel to that of the widely known and used orthogonal polynomials, is explained here for the first time. Presentation of many new results in one place for the first time. First time coverage of skew-orthogonal and bi-orthogonal polynomials and their use in the evaluation of some multiple integrals. Fredholm determinants and Painlevé equations. The three Gaussian ensembles (unitary, orthogonal, and symplectic); their n-point correlations, spacing probabilities. Fredholm determinants and inverse scattering theory. Probability densities of random determinants.

Theory Of Linear Algebraic Equations With Random Coefficients

Author : Viacheslav Leonidovich Girko
ISBN : UOM:39015043106213
Genre : Mathematics
File Size : 22. 58 MB
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Combinatorics And Random Matrix Theory

Author : Jinho Baik
ISBN : 9780821848418
Genre : Combinatorial analysis
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Over the last fifteen years a variety of problems in combinatorics have been solved in terms of random matrix theory. More precisely, the situation is as follows: the problems at hand are probabilistic in nature and, in an appropriate scaling limit, it turns out that certain key quantities associated with these problems behave statistically like the eigenvalues of a (large) random matrix. Said differently, random matrix theory provides a “stochastic special function theory” for a broad and growing class of problems in combinatorics. The goal of this book is to analyze in detail two key examples of this phenomenon, viz., Ulam's problem for increasing subsequences of random permutations and domino tilings of the Aztec diamond. Other examples are also described along the way, but in less detail. Techniques from many different areas in mathematics are needed to analyze these problems. These areas include combinatorics, probability theory, functional analysis, complex analysis, and the theory of integrable systems. The book is self-contained, and along the way we develop enough of the theory we need from each area that a general reader with, say, two or three years experience in graduate school can learn the subject directly from the text.

Random Matrix Models And Their Applications

Author : Pavel Maximovich Bleher
ISBN : 0521802091
Genre : Mathematics
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Expository articles on random matrix theory emphasizing the exchange of ideas between the physical and mathematical communities.

Theory Of Stochastic Canonical Equations

Author : V.L. Girko
ISBN : 9789401009898
Genre : Mathematics
File Size : 55. 58 MB
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Theory of Stochastic Canonical Equations collects the major results of thirty years of the author's work in the creation of the theory of stochastic canonical equations. It is the first book to completely explore this theory and to provide the necessary tools for dealing with these equations. Included are limit phenomena of sequences of random matrices and the asymptotic properties of the eigenvalues of such matrices. The book is especially interesting since it gives readers a chance to study proofs written by the mathematician who discovered them. All fifty-nine canonical equations are derived and explored along with their applications in such diverse fields as probability and statistics, economics and finance, statistical physics, quantum mechanics, control theory, cryptography, and communications networks. Some of these equations were first published in Russian in 1988 in the book Spectral Theory of Random Matrices, published by Nauka Science, Moscow. An understanding of the structure of random eigenvalues and eigenvectors is central to random matrices and their applications. Random matrix analysis uses a broad spectrum of other parts of mathematics, linear algebra, geometry, analysis, statistical physics, combinatories, and so forth. In return, random matrix theory is one of the chief tools of modern statistics, to the extent that at times the interface between matrix analysis and statistics is notably blurred. Volume I of Theory of Stochastic Canonical Equations discusses the key canonical equations in advanced random matrix analysis. Volume II turns its attention to a broad discussion of some concrete examples of matrices. It contains in-depth discussion of modern, highly-specialized topics in matrix analysis, such as unitary random matrices and Jacoby random matrices. The book is intended for a variety of readers: students, engineers, statisticians, economists and others.

Theory Of Random Functions And Its Application To Control Problems

Author : Vladimir Semenovich Pugachev
ISBN : UCAL:B4535579
Genre : Control theory
File Size : 31. 13 MB
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Probability Theory Random Processes And Mathematical Statistics

Author : IUrii A. Rozanov
ISBN : UOM:39015037306837
Genre : Mathematics
File Size : 38. 57 MB
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The second part (Chapters 4-6) provides a foundation of stochastic analysis, gives information on basic models of random processes and tools to study them. Here a certain familiarity with elements of functional analysis is necessary. Important material is presented in the form of examples to keep readers involved. Audience: This is a concise textbook for a graduate level course, with carefully selected topics representing the most important areas of modern probability, random processes and statistics.

A Survey On The Theory Of Random Equations

Author : Albert T. Bharucha-Reid
ISBN : UOM:39015017396675
Genre : Functional analysis
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International Aerospace Abstracts

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ISBN : STANFORD:36105007165322
Genre : Aeronautics
File Size : 73. 67 MB
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Recent Perspectives In Random Matrix Theory And Number Theory

Author : F. Mezzadri
ISBN : 0521620589
Genre : Mathematics
File Size : 66. 3 MB
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Provides a grounding in random matrix techniques applied to analytic number theory.

Statistical Theory And Method Abstracts

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ISBN : UCBK:C045054351
Genre : Statistics
File Size : 78. 31 MB
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Theory Of Probability And Mathematical Statistics

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ISBN : UCSD:31822017773466
Genre : Mathematical statistics
File Size : 77. 17 MB
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International Mathematical News

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ISBN : UCAL:B4591143
Genre : Mathematics
File Size : 46. 9 MB
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Asymptotic Theory Of Nonlinear Regression

Author : A. V. Ivanov
ISBN : UCSC:32106014263930
Genre : Language Arts & Disciplines
File Size : 73. 86 MB
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This book presents up-to-date mathematical results in asymptotic theory on nonlinear regression on the basis of various asymptotic expansions of least squares, its characteristics, and its distribution functions of functionals of Least Squares Estimator. It is divided into four chapters. In Chapter 1 assertions on the probability of large deviation of normal Least Squares Estimator of regression function parameters are made. Chapter 2 indicates conditions for Least Moduli Estimator asymptotic normality. An asymptotic expansion of Least Squares Estimator as well as its distribution function are obtained and two initial terms of these asymptotic expansions are calculated. Separately, the Berry-Esseen inequality for Least Squares Estimator distribution is deduced. In the third chapter asymptotic expansions related to functionals of Least Squares Estimator are dealt with. Lastly, Chapter 4 offers a comparison of the powers of statistical tests based on Least Squares Estimators. The Appendix gives an overview of subsidiary facts and a list of principal notations. Additional background information, grouped per chapter, is presented in the Commentary section. The volume concludes with an extensive Bibliography. Audience: This book will be of interest to mathematicians and statisticians whose work involves stochastic analysis, probability theory, mathematics of engineering, mathematical modelling, systems theory or cybernetics.

Wiley Encyclopedia Of Electrical And Electronics Engineering 24 Volume Set Plus Supplement 1

Author : John G. Webster
ISBN : 0471390526
Genre : Technology & Engineering
File Size : 48. 55 MB
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The Wiley Encyclopedia of Electrical and Electronics Engineering, edited by John G. Webster, remains the most comprehensive and authoritative resource in the electrical and electronics engineering field to date: Each article has been written by expert in the field or discipline Articles are structured to start with basic material and then move on to more complex theory and applications All articles have been cross-referenced to related literature of further research Covers the history of electrical and electronics engineering, patents, computer engineering and much more Wiley is committed to ensuring that the online version of the Encyclopedia continues to reflect the state-of-the-art in engineering and computer science through frequently updating and expanding the Encyclopedia www.wileyonlinelibrary.com/ref/eeee 24 Volumes plus supplement

Bulletin

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ISBN : UCAL:B4165886
Genre :
File Size : 54. 60 MB
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Mathematical Reviews

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ISBN : UOM:39015065183579
Genre : Mathematics
File Size : 22. 4 MB
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Russian Mathematical Surveys

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ISBN : UCAL:B3006250
Genre : Mathematicians
File Size : 24. 98 MB
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Multiple Access In Connectionless Networks Using Cooperative Transmission

Author : Atul Salhotra
ISBN : CORNELL:31924098293420
Genre :
File Size : 80. 97 MB
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