Ergodic Theory

Independence and Dichotomies

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Author: David Kerr,Hanfeng Li

Publisher: Springer

ISBN: 3319498479

Category: Mathematics

Page: 431

View: 8642

This book provides an introduction to the ergodic theory and topological dynamics of actions of countable groups. It is organized around the theme of probabilistic and combinatorial independence, and highlights the complementary roles of the asymptotic and the perturbative in its comprehensive treatment of the core concepts of weak mixing, compactness, entropy, and amenability. The more advanced material includes Popa's cocycle superrigidity, the Furstenberg-Zimmer structure theorem, and sofic entropy. The structure of the book is designed to be flexible enough to serve a variety of readers. The discussion of dynamics is developed from scratch assuming some rudimentary functional analysis, measure theory, and topology, and parts of the text can be used as an introductory course. Researchers in ergodic theory and related areas will also find the book valuable as a reference.

Fractal Geometry and Stochastics IV

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Author: Christoph Bandt,Peter Mörters,Martina Zähle

Publisher: Springer Science & Business Media

ISBN: 9783034600309

Category: Mathematics

Page: 290

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Over the last fifteen years fractal geometry has established itself as a substantial mathematical theory in its own right. The interplay between fractal geometry, analysis and stochastics has highly influenced recent developments in mathematical modeling of complicated structures. This process has been forced by problems in these areas related to applications in statistical physics, biomathematics and finance. This book is a collection of survey articles covering many of the most recent developments, like Schramm-Loewner evolution, fractal scaling limits, exceptional sets for percolation, and heat kernels on fractals. The authors were the keynote speakers at the conference "Fractal Geometry and Stochastics IV" at Greifswald in September 2008.

First European Congress of Mathematics Paris, July 6-10, 1992

Vol. II: Invited Lectures

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Author: Anthony Joseph,Fulbert Mignot,Francois Murat,Bernard Prum,Rudolf Rentschler

Publisher: Nelson Thornes

ISBN: 9783764327996

Category: Mathematics

Page: 513

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Table of Contents: D. Duffie: Martingales, Arbitrage, and Portfolio Choice • J. Fröhlich: Mathematical Aspects of the Quantum Hall Effect • M. Giaquinta: Analytic and Geometric Aspects of Variational Problems for Vector Valued Mappings • U. Hamenstädt: Harmonic Measures for Leafwise Elliptic Operators Along Foliations • M. Kontsevich: Feynman Diagrams and Low-Dimensional Topology • S.B. Kuksin: KAM-Theory for Partial Differential Equations • M. Laczkovich: Paradoxical Decompositions: A Survey of Recent Results • J.-F. Le Gall: A Path-Valued Markov Process and its Connections with Partial Differential Equations • I. Madsen: The Cyclotomic Trace in Algebraic K-Theory • A.S. Merkurjev: Algebraic K-Theory and Galois Cohomology • J. Nekovár: Values of L-Functions and p-Adic Cohomology • Y.A. Neretin: Mantles, Trains and Representations of Infinite Dimensional Groups • M.A. Nowak: The Evolutionary Dynamics of HIV Infections • R. Piene: On the Enumeration of Algebraic Curves - from Circles to Instantons • A. Quarteroni: Mathematical Aspects of Domain Decomposition Methods • A. Schrijver: Paths in Graphs and Curves on Surfaces • B. Silverman: Function Estimation and Functional Data Analysis • V. Strassen: Algebra and Complexity • P. Tukia: Generalizations of Fuchsian and Kleinian Groups • C. Viterbo: Properties of Embedded Lagrange Manifolds • D. Voiculescu: Alternative Entropies in Operator Algebras • M. Wodzicki : Algebraic K-Theory and Functional Analysis • D. Zagier: Values of Zeta Functions and Their Applications

C*-algebras and Finite-dimensional Approximations

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Author: Nathanial Patrick Brown,Narutaka Ozawa

Publisher: American Mathematical Soc.

ISBN: 0821843818

Category: Mathematics

Page: 509

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$\mathrm{C}^*$-approximation theory has provided the foundation for many of the most important conceptual breakthroughs and applications of operator algebras. This book systematically studies (most of) the numerous types of approximation properties that have been important in recent years: nuclearity, exactness, quasidiagonality, local reflexivity, and others. Moreover, it contains user-friendly proofs, insofar as that is possible, of many fundamental results that were previously quite hard to extract from the literature. Indeed, perhaps the most important novelty of the first ten chapters is an earnest attempt to explain some fundamental, but difficult and technical, results as painlessly as possible. The latter half of the book presents related topics and applications--written with researchers and advanced, well-trained students in mind. The authors have tried to meet the needs both of students wishing to learn the basics of an important area of research as well as researchers who desire a fairly comprehensive reference for the theory and applications of $\mathrm{C}^*$-approximation theory.

Banach Algebras and Their Applications

Sixteenth International Conference on Banach Algebras, University of Alberta in Edmonton, Canada, July 27-August 9, 2003

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Author: Anthony To-Ming Lau,Volker Runde

Publisher: American Mathematical Soc.

ISBN: 0821834711

Category: Mathematics

Page: 343

View: 4468

This proceedings volume is from the international conference on Banach algebras and their applications held at the University of Alberta (Edmonton). It contains a collection of refereed research papers and high-level expository articles that offer a panorama of Banach algebra theory and its manifold applications. Topics in the book range from $K$-theory to abstract harmonic analysis to operator theory. It is suitable for graduate students and researchers interested in Banach algebras.

Groups St Andrews 2005:

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Author: C. M. Campbell

Publisher: Cambridge University Press

ISBN: 0521694698

Category: Mathematics

Page: 701

View: 845

Selected papers from 'Groups St Andrews 2005' cover a wide spectrum of modern group theory.