Random Walks On Reductive Groups

Author : Yves Benoist
Publisher : Springer
ISBN 13 : 3319477218
Total Pages : 323 pages
Book Rating : 4.13/5 ( download)

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Download or read book Random Walks on Reductive Groups written by Yves Benoist and published by Springer. This book was released on 2016-10-20 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical theory of random walks describes the asymptotic behavior of sums of independent identically distributed random real variables. This book explains the generalization of this theory to products of independent identically distributed random matrices with real coefficients. Under the assumption that the action of the matrices is semisimple – or, equivalently, that the Zariski closure of the group generated by these matrices is reductive - and under suitable moment assumptions, it is shown that the norm of the products of such random matrices satisfies a number of classical probabilistic laws. This book includes necessary background on the theory of reductive algebraic groups, probability theory and operator theory, thereby providing a modern introduction to the topic.

Author : Steven P. Lalley
Publisher : Springer Nature
ISBN 13 : 3031256328
Total Pages : 373 pages
Book Rating : 4.25/5 ( download)

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Download or read book Random Walks on Infinite Groups written by Steven P. Lalley and published by Springer Nature. This book was released on 2023-05-08 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents the basic theory of random walks on infinite, finitely generated groups, along with certain background material in measure-theoretic probability. The main objective is to show how structural features of a group, such as amenability/nonamenability, affect qualitative aspects of symmetric random walks on the group, such as transience/recurrence, speed, entropy, and existence or nonexistence of nonconstant, bounded harmonic functions. The book will be suitable as a textbook for beginning graduate-level courses or independent study by graduate students and advanced undergraduate students in mathematics with a solid grounding in measure theory and a basic familiarity with the elements of group theory. The first seven chapters could also be used as the basis for a short course covering the main results regarding transience/recurrence, decay of return probabilities, and speed. The book has been organized and written so as to be accessible not only to students in probability theory, but also to students whose primary interests are in geometry, ergodic theory, or geometric group theory.

Author : M. Picardello
Publisher : Cambridge University Press
ISBN 13 : 9780521773126
Total Pages : 378 pages
Book Rating : 4.21/5 ( download)

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Download or read book Random Walks and Discrete Potential Theory written by M. Picardello and published by Cambridge University Press. This book was released on 1999-11-18 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive and interdisciplinary text covering the interplay between random walks and structure theory.

Author : Vadim Kaimanovich
Publisher : Walter de Gruyter
ISBN 13 : 3110198088
Total Pages : 545 pages
Book Rating : 4.89/5 ( download)

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Download or read book Random Walks and Geometry written by Vadim Kaimanovich and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Die jüngsten Entwicklungen zeigen, dass sich Wahrscheinlichkeitsverfahren zu einem sehr wirkungsvollen Werkzeug entwickelt haben, und das auf so unterschiedlichen Gebieten wie statistische Physik, dynamische Systeme, Riemann'sche Geometrie, Gruppentheorie, harmonische Analyse, Graphentheorie und Informatik.

Author : Laurent Bartholdi
Publisher : Springer Science & Business Media
ISBN 13 : 3764374470
Total Pages : 419 pages
Book Rating : 4.71/5 ( download)

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Download or read book Infinite Groups: Geometric, Combinatorial and Dynamical Aspects written by Laurent Bartholdi and published by Springer Science & Business Media. This book was released on 2006-03-28 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a panorama of recent advances in the theory of infinite groups. It contains survey papers contributed by leading specialists in group theory and other areas of mathematics. Topics include amenable groups, Kaehler groups, automorphism groups of rooted trees, rigidity, C*-algebras, random walks on groups, pro-p groups, Burnside groups, parafree groups, and Fuchsian groups. The accent is put on strong connections between group theory and other areas of mathematics.

Author : João Lopes Dias
Publisher : Springer Nature
ISBN 13 : 3031413164
Total Pages : 184 pages
Book Rating : 4.62/5 ( download)

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Download or read book New Trends in Lyapunov Exponents written by João Lopes Dias and published by Springer Nature. This book was released on 2023-11-29 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents peer-reviewed surveys on new developments in the study of Lyapunov exponents in dynamical systems and its applications to other areas, such as mathematical physics. Written by leading experts in their fields, the contributions are based upon the presentations given by invited speakers at the “New Trends in Lyapunov Exponents” workshop held in Lisbon, Portugal, February 7–11, 2022. The works focus on the concept of Lyapunov exponents in their various manifestations in dynamical systems along with their applications to mathematical physics and other areas of mathematics. The papers reflect the spirit of the conference of promoting new connections among different subjects in dynamical systems. This volume aims primarily at researchers and graduate students working in dynamical systems and related fields, serving as an introduction to active fields of research and as a review of recent results as well.

Author : Yves Guivarc'h
Publisher : Springer Science & Business Media
ISBN 13 : 1461224527
Total Pages : 297 pages
Book Rating : 4.25/5 ( download)

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Download or read book Compactifications of Symmetric Spaces written by Yves Guivarc'h and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of symmetric space is of central importance in many branches of mathematics. Compactifications of these spaces have been studied from the points of view of representation theory, geometry, and random walks. This work is devoted to the study of the interrelationships among these various compactifications and, in particular, focuses on the martin compactifications. It is the first exposition to treat compactifications of symmetric spaces systematically and to uniformized the various points of view. The work is largely self-contained, with comprehensive references to the literature. It is an excellent resource for both researchers and graduate students.

Author : Semen Grigorʹevich Gindikin
Publisher : American Mathematical Soc.
ISBN 13 : 9780821834725
Total Pages : 372 pages
Book Rating : 4.2X/5 ( download)

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Download or read book Lie Groups and Symmetric Spaces written by Semen Grigorʹevich Gindikin and published by American Mathematical Soc.. This book was released on 2003 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Robert H. Gilman
Publisher : American Mathematical Soc.
ISBN 13 : 0821831585
Total Pages : 138 pages
Book Rating : 4.88/5 ( download)

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Download or read book Computational and Statistical Group Theory written by Robert H. Gilman and published by American Mathematical Soc.. This book was released on 2002 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a nice overview of the diversity of current trends in computational and statistical group theory. It presents the latest research and a number of specific topics, such as growth, black box groups, measures on groups, product replacement algorithms, quantum automata, and more. It includes contributions by speakers at AMS Special Sessions at The University of Nevada (Las Vegas) and the Stevens Institute of Technology (Hoboken, NJ). It is suitable for graduate students and research mathematicians interested in group theory.

Author : László Lovász
Publisher : Springer Science & Business Media
ISBN 13 : 3642392865
Total Pages : 714 pages
Book Rating : 4.63/5 ( download)

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Download or read book Erdös Centennial written by László Lovász and published by Springer Science & Business Media. This book was released on 2014-01-24 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paul Erdös was one of the most influential mathematicians of the twentieth century, whose work in number theory, combinatorics, set theory, analysis, and other branches of mathematics has determined the development of large areas of these fields. In 1999, a conference was organized to survey his work, his contributions to mathematics, and the far-reaching impact of his work on many branches of mathematics. On the 100th anniversary of his birth, this volume undertakes the almost impossible task to describe the ways in which problems raised by him and topics initiated by him (indeed, whole branches of mathematics) continue to flourish. Written by outstanding researchers in these areas, these papers include extensive surveys of classical results as well as of new developments.