Probability On Compact Lie Groups
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Probability On Compact Lie Groups
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Author : David Applebaum
language : en
Publisher: Springer
Release Date : 2014-06-26
Probability On Compact Lie Groups written by David Applebaum and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-26 with Mathematics categories.
Probability theory on compact Lie groups deals with the interaction between “chance” and “symmetry,” a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applications in statistics and engineering (particularly with respect to signal processing). The author gives a comprehensive introduction to some of the principle areas of study, with an emphasis on applicability. The most important topics presented are: the study of measures via the non-commutative Fourier transform, existence and regularity of densities, properties of random walks and convolution semigroups of measures and the statistical problem of deconvolution. The emphasis on compact (rather than general) Lie groups helps readers to get acquainted with what is widely seen as a difficult field but which is also justified by the wealth of interesting results at this level and the importance of these groups for applications. The book is primarily aimed at researchers working in probability, stochastic analysis and harmonic analysis on groups. It will also be of interest to mathematicians working in Lie theory and physicists, statisticians and engineers who are working on related applications. A background in first year graduate level measure theoretic probability and functional analysis is essential; a background in Lie groups and representation theory is certainly helpful but the first two chapters also offer orientation in these subjects.
Topics In Probability On Compact Lie Groups
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Author : Eric Michael Rains
language : en
Publisher:
Release Date : 1995
Topics In Probability On Compact Lie Groups written by Eric Michael Rains and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Lie groups categories.
L Vy Processes In Lie Groups
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Author : Ming Liao
language : en
Publisher: Cambridge University Press
Release Date : 2004-05-10
L Vy Processes In Lie Groups written by Ming Liao and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-05-10 with Mathematics categories.
The theory of Lévy processes in Lie groups is not merely an extension of the theory of Lévy processes in Euclidean spaces. Because of the unique structures possessed by non-commutative Lie groups, these processes exhibit certain interesting limiting properties which are not present for their counterparts in Euclidean spaces. These properties reveal a deep connection between the behaviour of the stochastic processes and the underlying algebraic and geometric structures of the Lie groups themselves. The purpose of this work is to provide an introduction to Lévy processes in general Lie groups, the limiting properties of Lévy processes in semi-simple Lie groups of non-compact type and the dynamical behavior of such processes as stochastic flows on certain homogeneous spaces. The reader is assumed to be familiar with Lie groups and stochastic analysis, but no prior knowledge of semi-simple Lie groups is required.
Harmonic Analysis On Semi Simple Lie Groups I
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Author : Garth Warner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Harmonic Analysis On Semi Simple Lie Groups I written by Garth Warner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The representation theory of locally compact groups has been vig orously developed in the past twenty-five years or so; of the various branches of this theory, one of the most attractive (and formidable) is the representation theory of semi-simple Lie groups which, to a great extent, is the creation of a single man: Harish-Chandra. The chief objective of the present volume and its immediate successor is to provide a reasonably self-contained introduction to Harish-Chandra's theory. Granting cer tain basic prerequisites (cf. infra), we have made an effort to give full details and complete proofs of the theorems on which the theory rests. The structure of this volume and its successor is as follows. Each book is divided into chapters; each chapter is divided into sections; each section into numbers. We then use the decimal system of reference; for example, 1. 3. 2 refers to the second number in the third section of the first chapter. Theorems, Propositions, Lemmas, and Corollaries are listed consecutively throughout any given number. Numbers which are set in fine print may be omitted at a first reading. There are a variety of Exam ples scattered throughout the text; the reader, if he is so inclined, can view them as exercises ad libitum. The Appendices to the text collect certain ancillary results which will be used on and off in the systematic exposi tion; a reference of the form A2.
Probabilities On The Heisenberg Group
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Author : Daniel Neuenschwander
language : en
Publisher: Springer
Release Date : 2006-11-14
Probabilities On The Heisenberg Group written by Daniel Neuenschwander and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The Heisenberg group comes from quantum mechanics and is the simplest non-commutative Lie group. While it belongs to the class of simply connected nilpotent Lie groups, it turns out that its special structure yields many results which (up to now) have not carried over to this larger class. This book is a survey of probabilistic results on the Heisenberg group. The emphasis lies on limit theorems and their relation to Brownian motion. Besides classical probability tools, non-commutative Fourier analysis and functional analysis (operator semigroups) comes in. The book is intended for probabilists and analysts interested in Lie groups, but given the many applications of the Heisenberg group, it will also be useful for theoretical phycisists specialized in quantum mechanics and for engineers.
Analysis On Lie Groups
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Author : Jacques Faraut
language : en
Publisher:
Release Date : 2008
Analysis On Lie Groups written by Jacques Faraut and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Lie algebras categories.
The Random Matrix Theory Of The Classical Compact Groups
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Author : Elizabeth S. Meckes
language : en
Publisher: Cambridge University Press
Release Date : 2019-08
The Random Matrix Theory Of The Classical Compact Groups written by Elizabeth S. Meckes and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08 with Mathematics categories.
Provides a comprehensive introduction to the theory of random orthogonal, unitary, and symplectic matrices.
It S Stochastic Calculus And Probability Theory
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Author : Nobuyuki Ikeda
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
It S Stochastic Calculus And Probability Theory written by Nobuyuki Ikeda and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Professor Kiyosi Ito is well known as the creator of the modern theory of stochastic analysis. Although Ito first proposed his theory, now known as Ito's stochastic analysis or Ito's stochastic calculus, about fifty years ago, its value in both pure and applied mathematics is becoming greater and greater. For almost all modern theories at the forefront of probability and related fields, Ito's analysis is indispensable as an essential instrument, and it will remain so in the future. For example, a basic formula, called the Ito formula, is well known and widely used in fields as diverse as physics and economics. This volume contains 27 papers written by world-renowned probability theorists. Their subjects vary widely and they present new results and ideas in the fields where stochastic analysis plays an important role. Also included are several expository articles by well-known experts surveying recent developments. Not only mathematicians but also physicists, biologists, economists and researchers in other fields who are interested in the effectiveness of stochastic theory will find valuable suggestions for their research. In addition, students who are beginning their study and research in stochastic analysis and related fields will find instructive and useful guidance here. This volume is dedicated to Professor Ito on the occasion of his eightieth birthday as a token of deep appreciation for his great achievements and contributions. An introduction to and commentary on the scientific works of Professor Ito are also included.
Analysis On Infinite Dimensional Lie Groups And Algebras Proceedings Of The International Colloquium
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Author : Jean Marion
language : en
Publisher: World Scientific
Release Date : 1998-10-30
Analysis On Infinite Dimensional Lie Groups And Algebras Proceedings Of The International Colloquium written by Jean Marion and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-30 with categories.
This proceedings volume can be considered as a monograph on the state-of-the-art in the wide range of analysis on infinite-dimensional algebraic-topological structures. Topics covered in this volume include integrability and regularity for Lie groups and Lie algebras, actions of infinite-dimensional Lie groups on manifolds of paths and related minimal orbits, quasi-invariant measures, white noise analysis, harmonic analysis on generalized convolution structures, and noncommutative geometry. A special feature of this volume is the interrelationship between problems of pure and applied mathematics and also between mathematics and physics.
International Encyclopedia Of Statistical Science
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Author : Miodrag Lovric
language : en
Publisher: Springer Nature
Release Date : 2025-06-19
International Encyclopedia Of Statistical Science written by Miodrag Lovric and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-19 with Mathematics categories.
The International Encyclopedia of Statistical Science stands as a monumental effort to enrich statistics education globally, particularly in regions facing educational challenges. By amalgamating the expertise of over 700 authors from 110 countries, including Nobel Laureates and presidents of statistical societies, it offers an unparalleled resource for readers worldwide. This encyclopedia is not just a collection of entries; it is a concerted effort to revive statistics as a vibrant, critical field of study and application. Providing a comprehensive and accessible account of statistical terms, methods, and applications, it enables readers to gain a quick insight into the subject, regardless of their background. This work serves to refresh and expand the knowledge of researchers, managers, and practitioners, highlighting the relevance and applicability of statistics across various fields, from economics and business to healthcare and public policy. Furthermore, it aims to inspire students by demonstrating the significance of statistics in solving real-world problems, thus encouraging a new generation to explore and contribute to the field.