Oxford: Oxford University Press, 2015. — 1068 p. With a foreword by Freeman Dyson, the handbook brings together leading mathematicians and physicists to offer a comprehensive overview of random matrix theory, including a guide to new developments and the diverse range of applications of this approach. In part one, all modern and classical techniques of solving random matrix models...
Springer, 2013. — 264 p. — ISBN: 3642388051, 9783642388057. Random Matrices are one of the major research areas in modern probability theory, due to their prominence in many different fields such as nuclear physics, statistics, telecommunication, free probability, non-commutative geometry, and dynamical systems. A great deal of recent work has focused on the study of spectra of...
Oxford: Oxford University Press, 2018. — 640 p. The field of stochastic processes and random matrix theory (RMT) has been a rapidly evolving subject during the last fifteen years. The continuous development and discovery of new tools, connections and ideas have led to an avalanche of new results. These breakthroughs have been made possible thanks, to a large extent, to the recent...
Cambridge: Cambridge University Press, 2009. — 510 p. Real and complex Wigner matrices. Hermite polynomials, spacings and limit distributions for the Gaussian ensembles. Some generalities. Free probability. Appendices. General conventions and notation.
World Scientific, 2009. — 174 p. — (Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore 18). — ISBN: 9814273112. Random matrix theory has a long history, beginning in the first instance in multivariate statistics. It was used by Wigner to supply explanations for the important regularity features of the apparently random dispositions of...
Singapore: World Scientific, 2014. — 233 p.
The book contains three parts: Spectral theory of large dimensional random matrices; Applications to wireless communications; and Applications to finance. In the first part, we introduce some basic theorems of spectral analysis of large dimensional random matrices that are obtained under finite moment conditions, such as the limiting...
Springer Series in Statistics. 2009. — 552 pages.
ISBN: 1441906606.
The aim of the book is to introduce basic concepts, main results, and widely applied mathematical tools in the spectral analysis of large dimensional random matrices. The core of the book focuses on results established under moment conditions on random variables using probabilistic methods, and is thus easily...
Milton: Chapman and Hall/CRC, 2018. — 297 p. Large Covariance and Autocovariance Matrices brings together a collection of recent results on sample covariance and autocovariance matrices in high-dimensional models and novel ideas on how to use them for statistical inference in one or more high-dimensional time series models. The prerequisites include knowledge of elementary...
Cambridge: Cambridge University Press, 2009. — 449 p.
An introduction to the behaviour of random matrices. Suitable for postgraduate students and non-experts.
Cambridge: Cambridge University Press, 2009. — 449 p. This book focuses on the behavior of large random matrices. Standard results are covered, and the presentation emphasizes elementary operator theory and differential equations, so as to be accessible to graduate students and other non-experts. The introductory chapters review material on Lie groups and probability measures...
Boca Raton, USA: CRC Press, Taylor & Francis Group, 2018. — 293 p. — ISBN10: 1138591467. Large dimensional random matrices (LDRM) with specific patterns arise in econometrics, computer science, mathematics, physics, and statistics. This book provides an easy initiation to LDRM. Through a unified approach, we investigate the existence and properties of the limiting spectral...
CRC Press, 2022. — 287 p. — ISBN 9780367705008. This is an introductory book on Non-Commutative Probability or Free Probability and Large Dimensional Random Matrices. Basic concepts of free probability are introduced by analogy with classical probability in a lucid and quick manner. It then develops the results on the convergence of large dimensional random matrices, with a...
Springer Nature Singapore Pte Ltd, 2016. — 143 p. — (Springer Briefs in Mathematical Physics. Volume19) — ISBN: 9811033153. Random matrix theory (RMT) has a long history, starting with the statistics of nuclear energy levels by Wigner, and it has found applications in wide areas of all sciences from mathematics to biology. The universality of properties derived from random...
Dordrecht: Springer, 2001. — 1009 p. 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...
Berlin: Springer, 2009. — 284 p. Random matrix theory has developed in the last few years, in connection with various fields of mathematics and physics. These notes emphasize the relation with the problem of enumerating complicated graphs, and the related large deviations questions. Such questions are also closely related with the asymptotic distribution of matrices, which is...
Philadelphia: American Mathematical Society, 1998. — 436 p. The main topic of this book is the deep relation between the spacings between zeros of zeta and $L$-functions and spacings between eigenvalues of random elements of large compact classical groups. This relation, the Montgomery-Odlyzko law, is shown to hold for wide classes of zeta and $L$-functions over finite fields. The...
Springer International Publishing AG, 2018. — 122 p. — (SpringerBriefs in Mathematical Physics 26) — ISBN: 331970883X. Modern developments of Random Matrix Theory as well as pedagogical approaches to the standard core of the discipline are surprisingly hard to find in a well-organized, readable and user-friendly fashion. This slim and agile book, written in a pedagogical and...
Cambridge: Cambridge University Press, 2019. — 225 p. — (Cambridge Tracts in Mathematics 218). — ISBN: 978-1-108-41952-9. This is the first book to provide a comprehensive overview of foundational results and recent progress in the study of random matrices from the classical compact groups, drawing on the subject's deep connections to geometry, analysis, algebra, physics, and...
3rd ed. — Academic Press, 2004. — 688 p. This book 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 mathematics and mathematical physics, such as nuclear excitations, ultrasonic resonances of structural materials, chaotic systems, the zeros of the Riemann and other...
3rd ed. — Academic Press, 2004. — 688 p.
This book 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 mathematics and mathematical physics, such as nuclear excitations, ultrasonic resonances of structural materials, chaotic systems, the zeros of the Riemann and...
Springer Science+Business Media LLC, 2017. — 343 p. — (Fields Institute Monographs 35) — ISBN: 1493969412. This volume opens the world of free probability to a wide variety of readers. From its roots in the theory of operator algebras, free probability has intertwined with non-crossing partitions, random matrices, applications in wireless communications, representation theory...
Philadelphia: American Mathematical Society, 2011. — 650 p. Random matrix theory is a wide and growing field with a variety of concepts, results, and techniques and a vast range of applications in mathematics and the related sciences. The book, written by well-known experts, offers beginners a fairly balanced collection of basic facts and methods (Part 1 on classical ensembles)...
Cambridge: Cambridge University Press, 2021. — 370 p. — ISBN: 1108488080. The real world is perceived and broken down as data, models and algorithms in the eyes of physicists and engineers. Data is noisy by nature and classical statistical tools have so far been successful in dealing with relatively smaller levels of randomness. The recent emergence of Big Data and the required...
Cambridge University Press, 2021. — 370 p. — ISBN 9781108768900. The real world is perceived and broken down as data, models and algorithms in the eyes of physicists and engineers. Data is noisy by nature and classical statistical tools have so far been successful in dealing with relatively smaller levels of randomness. The recent emergence of Big Data and the required...
Singapore: World Scientific Publishing Company, 2015. — 284 p. This book is aimed at graduate students and researchers who are interested in the probability limit theory of random matrices and random partitions. It mainly consists of three parts. Part I is a brief review of classical central limit theorems for sums of independent random variables, martingale differences...
Singapore: World Scientific Publishing Company, 2015. — 284 p.
This book is aimed at graduate students and researchers who are interested in the probability limit theory of random matrices and random partitions. It mainly consists of three parts. Part I is a brief review of classical central limit theorems for sums of independent random variables, martingale differences...
Providence: American Mathematical Society, 2012. — 298 p. The field of random matrix theory has seen an explosion of activity in recent years, with connections to many areas of mathematics and physics. However, this makes the current state of the field almost too large to survey in a single book. In this graduate text, we focus on one specific sector of the field, namely the...
Providence: American Mathematical Society, 2014. — 186 p. The theory of random matrices is an amazingly rich topic in mathematics. Random matrices play a fundamental role in various areas such as statistics, mathematical physics, combinatorics, theoretical computer science, number theory and numerical analysis. This volume is based on lectures delivered at the 2013 AMS Short...
М.: Наука, Главная редакция физико-математической литературы, 1988. — (Теория вероятностей и математическая статистика). — 376 с. — ISBN 5-02-013749-9. Исследованы распределения собственных чисел и собственных векторов основных типов случайных матриц и матричных случайных процессов с аддитивными независимыми приращениями при предположении, что распределения матриц абсолютно...
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