Probability on Real Lie Algebras

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Author: Uwe Franz,Nicolas Privault

Publisher: Cambridge University Press

ISBN: 110712865X

Category: Mathematics

Page: 302

View: 1575

This monograph is a progressive introduction to non-commutativity in probability theory, summarizing and synthesizing recent results about classical and quantum stochastic processes on Lie algebras. In the early chapters, focus is placed on concrete examples of the links between algebraic relations and the moments of probability distributions. The subsequent chapters are more advanced and deal with Wigner densities for non-commutative couples of random variables, non-commutative stochastic processes with independent increments (quantum Lévy processes), and the quantum Malliavin calculus. This book will appeal to advanced undergraduate and graduate students interested in the relations between algebra, probability, and quantum theory. It also addresses a more advanced audience by covering other topics related to non-commutativity in stochastic calculus, Lévy processes, and the Malliavin calculus.

The Mathieu Groups

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Author: A. A. Ivanov

Publisher: Cambridge University Press

ISBN: 1108429785

Category: Mathematics

Page: 186

View: 558

The Mathieu Groups are presented in the context of finite geometry and the theory of group amalgams.

Dynamical Systems and Semisimple Groups

An Introduction

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Author: Renato Feres,RENATO AUTOR FERES

Publisher: Cambridge University Press

ISBN: 9780521591621

Category: Mathematics

Page: 245

View: 9899

This book comprises a systematic, self-contained introduction to the Margulis-Zimmer theory and provides an entry into current research. Taking as prerequisites only the standard first-year graduate courses in mathematics, the author develops in a detailed and self-contained way the main results on Lie groups, Lie algebras, and semisimple groups, including basic facts normally covered in first courses on manifolds and Lie groups plus topics such as integration of infinitesimal actions of Lie groups. He then derives the basic structure theorems for the real semisimple Lie groups, such as the Cartan and Iwasawa decompositions, and gives an extensive exposition of the general facts and concepts from topological dynamics and ergodic theory, including detailed proofs of the multiplicative ergodic theorem and Moore's ergodicity theorem.

Annales de l'I.H.P.

Probabilités et statistiques

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 6089

Bulletin

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 2221

Analysis and Geometry on Groups

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Author: Nicholas T. Varopoulos,L. Saloff-Coste,T. Coulhon

Publisher: Cambridge University Press

ISBN: 9780521088015

Category: Mathematics

Page: 172

View: 9778

The geometry and analysis that is discussed in this book extends to classical results for general discrete or Lie groups, and the methods used are analytical, but are not concerned with what is described these days as real analysis. Most of the results described in this book have a dual formulation: they have a "discrete version" related to a finitely generated discrete group and a continuous version related to a Lie group. The authors chose to center this book around Lie groups, but could easily have pushed it in several other directions as it interacts with the theory of second order partial differential operators, and probability theory, as well as with group theory.

Choice

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Academic libraries

Page: N.A

View: 9860

Hans Freudenthal

selecta

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Author: Hans Freudenthal,Tonny Albert Springer,Dirk Dalen

Publisher: European Mathematical Society

ISBN: 9783037190586

Category: Mathematics

Page: 653

View: 8791

Spinors in Hilbert Space

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Author: Roger Plymen,Paul Robinson

Publisher: Cambridge University Press

ISBN: 9780521450225

Category: Mathematics

Page: 165

View: 4771

A definitive self-contained account of the subject. Of appeal to a wide audience in mathematics and physics.

Non-homogeneous Random Walks

Lyapunov Function Methods for Near-Critical Stochastic Systems

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Author: Mikhail Menshikov,Serguei Popov,Andrew Wade

Publisher: Cambridge University Press

ISBN: 1316867366

Category: Mathematics

Page: N.A

View: 5009

Stochastic systems provide powerful abstract models for a variety of important real-life applications: for example, power supply, traffic flow, data transmission. They (and the real systems they model) are often subject to phase transitions, behaving in one way when a parameter is below a certain critical value, then switching behaviour as soon as that critical value is reached. In a real system, we do not necessarily have control over all the parameter values, so it is important to know how to find critical points and to understand system behaviour near these points. This book is a modern presentation of the 'semimartingale' or 'Lyapunov function' method applied to near-critical stochastic systems, exemplified by non-homogeneous random walks. Applications treat near-critical stochastic systems and range across modern probability theory from stochastic billiards models to interacting particle systems. Spatially non-homogeneous random walks are explored in depth, as they provide prototypical near-critical systems.

Zahlentheorie

Algebraische Zahlen und Funktionen

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Author: Helmut Koch

Publisher: Springer-Verlag

ISBN: 3322803120

Category: Mathematics

Page: 344

View: 985

Hauptziel des Buches ist die Vermittlung des Grundbestandes der Algebraischen Zahlentheorie einschließlich der Theorie der normalen Erweiterungen bis hin zu einem Ausblick auf die Klassenkörpertheorie. Gleichberechtigt mit algebraischen Zahlen werden auch algebraische Funktionen behandelt. Dies geschieht einerseits um die Analogie zwischen Zahl- und Funktionenkörpern aufzuzeigen, die besonders deutlich im Falle eines endlichen Konstantenkörpers ist. Andererseits erhält man auf diese Weise eine Einführung in die Theorie der "höheren Kongruenzen" als eines wesentlichen Bestandteils der "Arithmetischen Geometrie". Obgleich das Buch hauptsächlich algebraischen Methoden gewidmet ist, findet man in der Einleitung auch einen kurzen Beweis des Primzahlsatzes nach Newman. In den Kapiteln 7 und 8 wird die Theorie der Heckeschen L-Reihen behandelt einschließlich der Verteilung der Primideale algebraischer Zahlkörper in Kegeln.

Books in Print

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 5036

Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

Universal Biography

Containing a Copious Account, Critical and Historical, of the Life and Character, Labors and Actions of Eminent Persons, in All Ages and Countries, Conditions and Professions ...

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Author: John Lemprière

Publisher: N.A

ISBN: N.A

Category: Biography

Page: N.A

View: 9251