Topics In Probability And Lie Groups

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Topics in Probability and Lie Groups: Boundary Theory

John Christopher Taylor
Topics in Probability and Lie Groups Boundary Theory Book PDF

Author : John Christopher Taylor
Publisher : American Mathematical Soc.
Page : 214 pages
File Size : 52,7 Mb
Release : 2001
Category : Lie groups
ISBN : 9780821802755

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Topics in Probability and Lie Groups: Boundary Theory by John Christopher Taylor Pdf

This volume is comprised of two parts: the first contains articles by S. N. Evans, F. Ledrappier, and Figa-Talomanaca. These articles arose from a Centre de Recherches de Mathematiques (CRM) seminar entitiled, ``Topics in Probability on Lie Groups: Boundary Theory''. Evans gives a synthesis of his pre-1992 work on Gaussian measures on vector spaces over a local field. Ledrappier uses the freegroup on $d$ generators as a paradigm for results on the asymptotic properties of random walks and harmonic measures on the Martin boundary. These articles are followed by a case study by Figa-Talamanca using Gelfand pairs to study a diffusion on a compact ultrametric space. The second part of the book is an appendix to the book Compactifications of Symmetric Spaces (Birkhauser) by Y. Guivarc'h and J. C. Taylor. This appendix consists of an article by each author and presents the contents of this book in a more algebraic way. L. Ji and J.-P. Anker simplifies some of their results on the asymptotics of the Green function that were used to compute Martin boundaries. And Taylor gives a self-contained account of Martin boundary theory for manifolds using the theory of second order strictly elliptic partial differential operators.

Probability on Compact Lie Groups

David Applebaum
Probability on Compact Lie Groups Book PDF

Author : David Applebaum
Publisher : Springer
Page : 217 pages
File Size : 46,6 Mb
Release : 2014-06-26
Category : Mathematics
ISBN : 9783319078427

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Probability on Compact Lie Groups by David Applebaum Pdf

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.

Stochastic Models, Information Theory, and Lie Groups, Volume 1

Gregory S. Chirikjian
Stochastic Models Information Theory and Lie Groups Volume 1 Book PDF

Author : Gregory S. Chirikjian
Publisher : Springer Science & Business Media
Page : 397 pages
File Size : 47,8 Mb
Release : 2009-09-02
Category : Mathematics
ISBN : 9780817648039

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Stochastic Models, Information Theory, and Lie Groups, Volume 1 by Gregory S. Chirikjian Pdf

This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering. Extensive exercises and motivating examples make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.

Invariant Markov Processes Under Lie Group Actions

Ming Liao
Invariant Markov Processes Under Lie Group Actions Book PDF

Author : Ming Liao
Publisher : Springer
Page : 363 pages
File Size : 41,8 Mb
Release : 2018-06-28
Category : Mathematics
ISBN : 9783319923246

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Invariant Markov Processes Under Lie Group Actions by Ming Liao Pdf

The purpose of this monograph is to provide a theory of Markov processes that are invariant under the actions of Lie groups, focusing on ways to represent such processes in the spirit of the classical Lévy-Khinchin representation. It interweaves probability theory, topology, and global analysis on manifolds to present the most recent results in a developing area of stochastic analysis. The author’s discussion is structured with three different levels of generality:— A Markov process in a Lie group G that is invariant under the left (or right) translations— A Markov process xt in a manifold X that is invariant under the transitive action of a Lie group G on X— A Markov process xt invariant under the non-transitive action of a Lie group GA large portion of the text is devoted to the representation of inhomogeneous Lévy processes in Lie groups and homogeneous spaces by a time dependent triple through a martingale property. Preliminary definitions and results in both stochastics and Lie groups are provided in a series of appendices, making the book accessible to those who may be non-specialists in either of these areas. Invariant Markov Processes Under Lie Group Actions will be of interest to researchers in stochastic analysis and probability theory, and will also appeal to experts in Lie groups, differential geometry, and related topics interested in applications of their own subjects.

Stochastic Models, Information Theory, and Lie Groups, Volume 2

Gregory S. Chirikjian
Stochastic Models Information Theory and Lie Groups Volume 2 Book PDF

Author : Gregory S. Chirikjian
Publisher : Springer Science & Business Media
Page : 461 pages
File Size : 45,8 Mb
Release : 2011-11-16
Category : Mathematics
ISBN : 9780817649449

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Stochastic Models, Information Theory, and Lie Groups, Volume 2 by Gregory S. Chirikjian Pdf

This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering. Extensive exercises, motivating examples, and real-world applications make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.

Lie Groups and Symmetric Spaces

Semen Grigorʹevich Gindikin
Lie Groups and Symmetric Spaces Book PDF

Author : Semen Grigorʹevich Gindikin
Publisher : American Mathematical Soc.
Page : 372 pages
File Size : 52,6 Mb
Release : 2003
Category : Geometry, Differential
ISBN : 082183472X

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Lie Groups and Symmetric Spaces by Semen Grigorʹevich Gindikin Pdf

The book contains survey and research articles devoted mainly to geometry and harmonic analysis of symmetric spaces and to corresponding aspects of group representation theory. The volume is dedicated to the memory of Russian mathematician, F. I. Karpelevich (1927-2000). Of particular interest are the survey articles by Sawyer on the Abel transform on noncompact Riemannian symmetric spaces, and by Anker and Ostellari on estimates for heat kernels on such spaces, as well as thearticle by Bernstein and Gindikin on integral geometry for families of curves. There are also many research papers on topics of current interest. The book is suitable for graduate students and research mathematicians interested in harmonic analysis and representation theory.

Probabilities on the Heisenberg Group

Daniel Neuenschwander
Probabilities on the Heisenberg Group Book PDF

Author : Daniel Neuenschwander
Publisher : Springer
Page : 146 pages
File Size : 40,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540685906

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Probabilities on the Heisenberg Group by Daniel Neuenschwander Pdf

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

Jacques Faraut
Analysis on Lie Groups Book PDF

Author : Jacques Faraut
Publisher : Cambridge University Press
Page : 314 pages
File Size : 54,6 Mb
Release : 2008-05-22
Category : Mathematics
ISBN : 0521719305

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Analysis on Lie Groups by Jacques Faraut Pdf

This self-contained text concentrates on the perspective of analysis, assuming only elementary knowledge of linear algebra and basic differential calculus. The author describes, in detail, many interesting examples, including formulas which have not previously appeared in book form. Topics covered include the Haar measure and invariant integration, spherical harmonics, Fourier analysis and the heat equation, Poisson kernel, the Laplace equation and harmonic functions. Perfect for advanced undergraduates and graduates in geometric analysis, harmonic analysis and representation theory, the tools developed will also be useful for specialists in stochastic calculation and the statisticians. With numerous exercises and worked examples, the text is ideal for a graduate course on analysis on Lie groups.

An Introduction to Lie Groups and Lie Algebras

Alexander A. Kirillov
An Introduction to Lie Groups and Lie Algebras Book PDF

Author : Alexander A. Kirillov
Publisher : Cambridge University Press
Page : 237 pages
File Size : 40,7 Mb
Release : 2008-07-31
Category : Mathematics
ISBN : 9780521889698

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An Introduction to Lie Groups and Lie Algebras by Alexander A. Kirillov Pdf

Contemporary introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples

Discrete Subgroups of Semisimple Lie Groups

Gregori A. Margulis
Discrete Subgroups of Semisimple Lie Groups Book PDF

Author : Gregori A. Margulis
Publisher : Springer Science & Business Media
Page : 408 pages
File Size : 42,9 Mb
Release : 1991-02-15
Category : Mathematics
ISBN : 354012179X

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Discrete Subgroups of Semisimple Lie Groups by Gregori A. Margulis Pdf

Discrete subgroups have played a central role throughout the development of numerous mathematical disciplines. Discontinuous group actions and the study of fundamental regions are of utmost importance to modern geometry. Flows and dynamical systems on homogeneous spaces have found a wide range of applications, and of course number theory without discrete groups is unthinkable. This book, written by a master of the subject, is primarily devoted to discrete subgroups of finite covolume in semi-simple Lie groups. Since the notion of "Lie group" is sufficiently general, the author not only proves results in the classical geometry setting, but also obtains theorems of an algebraic nature, e.g. classification results on abstract homomorphisms of semi-simple algebraic groups over global fields. The treatise of course contains a presentation of the author's fundamental rigidity and arithmeticity theorems. The work in this monograph requires the language and basic results from fields such as algebraic groups, ergodic theory, the theory of unitary representatons, and the theory of amenable groups. The author develops the necessary material from these subjects; so that, while the book is of obvious importance for researchers working in related areas, it is essentially self-contained and therefore is also of great interest for advanced students.

Lévy Processes in Lie Groups

Ming Liao
L vy Processes in Lie Groups Book PDF

Author : Ming Liao
Publisher : Cambridge University Press
Page : 292 pages
File Size : 51,5 Mb
Release : 2004-05-10
Category : Mathematics
ISBN : 0521836530

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Lévy Processes in Lie Groups by Ming Liao Pdf

Up-to-the minute research on important stochastic processes.

Stochastic Models, Information Theory, and Lie Groups, Volume 2

Gregory S. Chirikjian
Stochastic Models Information Theory and Lie Groups Volume 2 Book PDF

Author : Gregory S. Chirikjian
Publisher : Springer Science & Business Media
Page : 460 pages
File Size : 55,5 Mb
Release : 2011-11-15
Category : Mathematics
ISBN : 9780817649432

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Stochastic Models, Information Theory, and Lie Groups, Volume 2 by Gregory S. Chirikjian Pdf

This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering. Extensive exercises, motivating examples, and real-world applications make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.

Probability Measures on Groups X

H. Heyer
Probability Measures on Groups X Book PDF

Author : H. Heyer
Publisher : Springer Science & Business Media
Page : 491 pages
File Size : 47,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781489923646

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Probability Measures on Groups X by H. Heyer Pdf

The present volume contains the transactions of the lOth Oberwolfach Conference on "Probability Measures on Groups". The series of these meetings inaugurated in 1970 by L. Schmetterer and the editor is devoted to an intensive exchange of ideas on a subject which developed from the relations between various topics of mathematics: measure theory, probability theory, group theory, harmonic analysis, special functions, partial differential operators, quantum stochastics, just to name the most significant ones. Over the years the fruitful interplay broadened in various directions: new group-related structures such as convolution algebras, generalized translation spaces, hypercomplex systems, and hypergroups arose from generalizations as well as from applications, and a gradual refinement of the combinatorial, Banach-algebraic and Fourier analytic methods led to more precise insights into the theory. In a period of highest specialization in scientific thought the separated minds should be reunited by actively emphasizing similarities, analogies and coincidences between ideas in their fields of research. Although there is no real separation between one field and another - David Hilbert denied even the existence of any difference between pure and applied mathematics - bridges between probability theory on one side and algebra, topology and geometry on the other side remain absolutely necessary. They provide a favorable ground for the communication between apparently disjoint research groups and motivate the framework of what is nowadays called "Structural probability theory".

Topics in Groups and Geometry

Tullio Ceccherini-Silberstein,Michele D'Adderio
Topics in Groups and Geometry Book PDF

Author : Tullio Ceccherini-Silberstein,Michele D'Adderio
Publisher : Springer Nature
Page : 468 pages
File Size : 41,7 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9783030881092

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Topics in Groups and Geometry by Tullio Ceccherini-Silberstein,Michele D'Adderio Pdf

This book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov’s pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at asymptotic cones, and a discussion of related subjects including filters and ultrafilters, dimension theory, hyperbolic geometry, amenability, the Burnside problem, and random walks on groups. The results are unified under the common theme of Gromov’s theorem, namely that finitely generated groups of polynomial growth are virtually nilpotent. This beautiful result gave birth to a fascinating new area of research which is still active today. The purpose of the book is to collect these naturally related results together in one place, most of which are scattered throughout the literature, some of them appearing here in book form for the first time. In this way, the connections between these topics are revealed, providing a pleasant introduction to geometric group theory based on ideas surrounding Gromov's theorem. The book will be of interest to mature undergraduate and graduate students in mathematics who are familiar with basic group theory and topology, and who wish to learn more about geometric, analytic, and probabilistic aspects of infinite groups.

An Introduction to Lie Groups and the Geometry of Homogeneous Spaces

Andreas Arvanitogeōrgos
An Introduction to Lie Groups and the Geometry of Homogeneous Spaces Book PDF

Author : Andreas Arvanitogeōrgos
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 48,9 Mb
Release : 2003
Category : Homogeneous spaces
ISBN : 9780821827789

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An Introduction to Lie Groups and the Geometry of Homogeneous Spaces by Andreas Arvanitogeōrgos Pdf

It is remarkable that so much about Lie groups could be packed into this small book. But after reading it, students will be well-prepared to continue with more advanced, graduate-level topics in differential geometry or the theory of Lie groups. The theory of Lie groups involves many areas of mathematics. In this book, Arvanitoyeorgos outlines enough of the prerequisites to get the reader started. He then chooses a path through this rich and diverse theory that aims for an understanding of the geometry of Lie groups and homogeneous spaces. In this way, he avoids the extra detail needed for a thorough discussion of other topics. Lie groups and homogeneous spaces are especially useful to study in geometry, as they provide excellent examples where quantities (such as curvature) are easier to compute. A good understanding of them provides lasting intuition, especially in differential geometry. The book is suitable for advanced undergraduates, graduate students, and research mathematicians interested in differential geometry and neighboring fields, such as topology, harmonic analysis, and mathematical physics.