Random Walks on Infinite Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Random Walks on Infinite Groups write by Steven P. Lalley. This book was released on 2023-05-08. Random Walks on Infinite Groups available in PDF, EPUB and Kindle. 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.
Random Walks and Geometry
Random Walks and Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Random Walks and Geometry write by Vadim Kaimanovich. This book was released on 2008-08-22. Random Walks and Geometry available in PDF, EPUB and Kindle. 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.
Combinatorial and Computational Geometry
Combinatorial and Computational Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Combinatorial and Computational Geometry write by Jacob E. Goodman. This book was released on 2005-08-08. Combinatorial and Computational Geometry available in PDF, EPUB and Kindle. This 2005 book deals with interest topics in Discrete and Algorithmic aspects of Geometry.
Topics in Groups and Geometry
Topics in Groups and Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topics in Groups and Geometry write by Tullio Ceccherini-Silberstein. This book was released on 2022-01-01. Topics in Groups and Geometry available in PDF, EPUB and Kindle. 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.
Random Walks and Geometry
Random Walks and Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Random Walks and Geometry write by Vadim A. Kaimanovich. This book was released on 2004. Random Walks and Geometry available in PDF, EPUB and Kindle. Recent developments show that probability methods have become a very powerful tool in such different areas as statistical physics, dynamical systems, Riemannian geometry, group theory, harmonic analysis, graph theory and computer science. This volume is an outcome of the special semester 2001 - Random Walks held at the Schrodinger Institute in Vienna, Austria. It contains original research articles with non-trivial new approaches based on applications of random walks and similar processes to Lie groups, geometric flows, physical models on infinite graphs, random number generators, Lyapunov exponents, geometric group theory, spectral theory of graphs and potential theory. Highlights are the first survey of the theory of the stochastic Loewner evolution and its applications to percolation theory (a new rapidly developing and very promising subject at the crossroads of probability, statistical physics and harmonic analysis), surveys on expander graphs, random matrices and quantum chaos, cellular automata and symbolic dynamical systems, and others. The contributors to the volume are the leading experts in the area."
