Series: Springer Series in Statistics
Originally published by Science Press, 2006. Science Press should be listed as a co-publisher in the FM but not the cover.
2010, Approx. 550 p., Hardcover
ISBN: 978-1-4419-0660-1
Due: February 2010
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 applicable to statistics and other areas of science. The book introduces fundamental results, most of them investigated by the authors, such as the semicircular law of Wigner matrices, the Marcenko-Pastur law, the limiting spectral distribution of the multivariate F matrix, limits of extreme eigenvalues, spectrum separation theorems, convergence rates of empirical distributions, central limit theorems of linear spectral statistics, and the partial solution of the famous circular law. While deriving the main results, the book simultaneously emphasizes the ideas and methodologies of the fundamental mathematical tools, among them being: truncation techniques, matrix identities, moment convergence theorems, and the Stieltjes transform. Its treatment is especially fitting to the needs of mathematics and statistics graduate students and beginning researchers, having a basic knowledge of matrix theory and an understanding of probability theory at the graduate level, who desire to learn the concepts and tools in solving problems in this area. It can also serve as a detailed handbook on results of large dimensional random matrices for practical users.
This second edition includes two additional chapters, one on the authors' results on the limiting behavior of eigenvectors of sample covariance matrices, another on applications to wireless communications and finance. While attempting to bring this edition up-to-date on recent work, it also provides summaries of other areas which are typically considered part of the general field of random matrix theory.
Introduction.- Wigner matrices and semicircular law.- Sample covariance matrices and the Marcenko-Pastur law.- Product of two random matrices.- Limits of extreme eigenvalues.- Spectrum separation.- Semicircle law for Hadamard products.- Convergence rates of ESD.- CLT for linear spectral statistics.- Eigenvectors of sample covariance matrices.- Circular law.- Some applications of RMT.
Series: Frontiers in Mathematics
2010, Approx. 500 p., Softcover
ISBN: 978-3-0346-0250-1
Due: March 2010
This book presents a comprehensive up-to-date research on the latest developments in differential geometry of lightlike (degenerate) subspaces. The main focus is on hypersurfaces and a variety of submanifolds of indefinite Kahlerian, Sasakian and quaternion Kahler manifolds. The primary objects of study are non-degenerate screen distributions, Cauchy-Rieman (CR) structures and their interrelated induced vector bundles. The book also contains several latest physical applications, ample solved examples and the subject matter is designed for a wider audience.
Graduate students, research associates and faculty working in differential geometry and mathematical physics
Preface.- Notations.- 1 Preliminaries.- 2 Lightlike hypersurfaces.- 3 Applications of lightlike hypersurfaces.- 4 Half-lightlike submanifolds.- 5 Lightlike submanifolds.- 6 Submanifolds of indefinite Kahler manifolds.- 7 Submanifolds of indefinite Sasakian manifolds.- 8 Submanifolds of Indefinite quaternion Kahler manifolds.- 9 Applications of lightlike geometry.- Bibliography.- Index.
2010, Approx. 1600 p. 335 illus. In 2 volumes, not available separately., Hardcover
ISBN: 978-0-387-77116-8
Due: March 2010
The lead editor, C.F. Lee, is one of the most prolific and well-known authors in the field
Quantitative finance is a combination of economics, accounting, statistics, econometrics, mathematics, stochastic process, and computer science and technology. Increasingly, the tools of financial analysis are being applied to assess, monitor, and mitigate risk, especially in the context of globalization, market volatility, and economic crisis. This three-volume handbook, compromised of over 100 chapters, is the most comprehensive resource in the field to date, integrating the most current theory, methodology, policy, and practical applications. Showcasing contributions from an international array of experts, the Handbook of Quantitative Finance and Risk Management is unparalleled in the breadth and depth of its coverage. Volume 1 presents an overview of quantitative finance and risk management research, covering the essential theories, policies, and empirical methodologies used in the field. Chapters provide in-depth discussion of portfolio theory and investment analysis. Volume 2 covers options and option pricing theory and risk management. Volume 3 presents a wide variety of models and analytical tools. Throughout, the handbook offers illustrative case examples, worked equations, and extensive references; additional features include chapter abstracts, keywords, and author and subject indices. From "arbitrage" to "yield spreads," the Handbook of Quantitative Finance and Risk Management will serve as an essential resource for academics, educators, students, policymakers, and practitioners.
Volume 1. Introduction.- Definitions.- Descriptive essays. Volume 2. Contributed papers.- Theories.- Methodologies.- Applications.- Appendix.- References.- Subject Index.- Author Index.
Series: Theoretical and Mathematical Physics
2010, Approx. 400 p., Hardcover
ISBN: 978-90-481-3644-5
Due: March 2010
Which problems do arise within relativistic enhancements of the Schrodinger theory, especially if one adheres to the usual one-particle interpretation, and to what extent can these problems be overcome? And what is the physical necessity of quantum field theories? In many books, answers to these fundamental questions are given highly insufficiently by treating the relativistic quantum mechanical one-particle concept very superficially and instead introducing field quantization as soon as possible. By contrast, this monograph emphasizes relativistic quantum mechanics in the narrow sense: it extensively discusses relativistic one-particle concepts and reveals their problems and limitations, therefore motivating the necessity of quantized fields in a physically comprehensible way.
The first chapters contain a detailed presentation and comparison of the Klein-Gordon and Dirac theory, always in view of the non-relativistic theory. In the third chapter, we consider relativistic scattering processes and develop the Feynman rules from propagator techniques. This is where the impossibility to get around a quantum field theoretical reasoning is discussed and basic quantum field theoretical concepts are introduced.
This book addresses undergraduate and graduate physics students who are interested in a clearly arranged and structured presentation of relativistic quantum mechanics in the "narrow sense" and its connection to quantum field theories. Each section contains a short summary and exercises with solutions. A mathematical appendix rounds up this excellent introductory book on relativistic quantum mechanics.
Undergraduate and graduate physics students as well as researchers in quantum physics who are interested in a clearly arranged and structured presentation of relativistic one particle quantum mechanics and its connection to quantum field theories
List of Exercises.- Preface.- 1. Relativistic Description of Spin-0 Particles.- 2. Relativistic Description of Spin-1/2 Particles.- 3. Relativistic Scattering Theory, Appendix.
Series: Trends in Mathematics
2010, Approx. 290 p., Hardcover
ISBN: 978-3-0346-0287-7
Due: April 2010
Affine flag manifolds are infinite dimensional versions of familiar objects such as Grasmann varieties. The book features lecture notes, survey articles, and research notes - based on workshops held in Berlin, Essen, and Madrid - explaining the significance of these and related objects (such as double affine Hecke algebras and affine Springer fibers) in representation theory (e.g., the theory of symmetric polynomials), arithmetic geometry (e.g., the fundamental lemma in the Langlands program), and algebraic geometry (e.g., affine flag manifolds as parameter spaces for principal bundles). Novel aspects of the theory of principal bundles on algebraic varieties are also studied in the book.
Advanced students and researchers in the areas of algebraic and arithmetic geometry and representation theory
U. Gortz: Affine Springer fibers and affine Deligne-Lusztig varieties; T. Gomez: Quantization of Hitchinfs integrable system and the geometric Langlands conjecture.- G. Hein: Faltingsf construction of the moduli space of vector bundles on a smooth projective curve.- J. Heinloth: Lectures on the moduli stack of vector bundles on a curve.- N. Hoffmann: On moduli stacks of G-bundles over a curve.- H. Lange, P. Newstead: Clifford indices for vector bundles on curves.- K.-G. Schlesinger: A physics perspective on geometric Langlands duality.- U. Stuhler: Unit groups of division algebras.- M. Varagnolo, E. Vasserot: Double affine Hecke algebras and affine flag manifolds, I