Random Walks And Geometry

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 : Jacob E. Goodman
Publisher : Cambridge University Press
ISBN 13 : 9780521848626
Total Pages : 640 pages
Book Rating : 4.28/5 ( download)

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Download or read book Combinatorial and Computational Geometry written by Jacob E. Goodman and published by Cambridge University Press. This book was released on 2005-08-08 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2005 book deals with interest topics in Discrete and Algorithmic aspects of Geometry.

Author : Wolfgang Woess
Publisher : Cambridge University Press
ISBN 13 : 0521552923
Total Pages : 350 pages
Book Rating : 4.29/5 ( download)

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Download or read book Random Walks on Infinite Graphs and Groups written by Wolfgang Woess and published by Cambridge University Press. This book was released on 2000-02-13 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme of this book is the interplay between the behaviour of a class of stochastic processes (random walks) and discrete structure theory. The author considers Markov chains whose state space is equipped with the structure of an infinite, locally finite graph, or as a particular case, of a finitely generated group. The transition probabilities are assumed to be adapted to the underlying structure in some way that must be specified precisely in each case. From the probabilistic viewpoint, the question is what impact the particular type of structure has on various aspects of the behaviour of the random walk. Vice-versa, random walks may also be seen as useful tools for classifying, or at least describing the structure of graphs and groups. Links with spectral theory and discrete potential theory are also discussed. This book will be essential reading for all researchers working in stochastic process and related topics.

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 : Vadim A. Kaimanovich
Publisher :
ISBN 13 : 9783119164269
Total Pages : 532 pages
Book Rating : 4.67/5 ( download)

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Download or read book Random Walks and Geometry written by Vadim A. Kaimanovich and published by . This book was released on 2004 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."

Author : Tullio Ceccherini-Silberstein
Publisher : Springer Nature
ISBN 13 : 3030881091
Total Pages : 468 pages
Book Rating : 4.92/5 ( download)

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Download or read book Topics in Groups and Geometry written by Tullio Ceccherini-Silberstein and published by Springer Nature. This book was released on 2022-01-01 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Gerald L. Alexanderson
Publisher : Cambridge University Press
ISBN 13 : 9780883855287
Total Pages : 324 pages
Book Rating : 4.83/5 ( download)

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Download or read book The Random Walks of George Polya written by Gerald L. Alexanderson and published by Cambridge University Press. This book was released on 2000-04-27 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Both a biography of Plya's life, and a review of his many mathematical achievements by today's experts.

Author : Asaf Nachmias
Publisher : Springer Nature
ISBN 13 : 3030279685
Total Pages : 120 pages
Book Rating : 4.84/5 ( download)

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Download or read book Planar Maps, Random Walks and Circle Packing written by Asaf Nachmias and published by Springer Nature. This book was released on 2019-10-04 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book focuses on the interplay between random walks on planar maps and Koebe’s circle packing theorem. Further topics covered include electric networks, the He–Schramm theorem on infinite circle packings, uniform spanning trees of planar maps, local limits of finite planar maps and the almost sure recurrence of simple random walks on these limits. One of its main goals is to present a self-contained proof that the uniform infinite planar triangulation (UIPT) is almost surely recurrent. Full proofs of all statements are provided. A planar map is a graph that can be drawn in the plane without crossing edges, together with a specification of the cyclic ordering of the edges incident to each vertex. One widely applicable method of drawing planar graphs is given by Koebe’s circle packing theorem (1936). Various geometric properties of these drawings, such as existence of accumulation points and bounds on the radii, encode important probabilistic information, such as the recurrence/transience of simple random walks and connectivity of the uniform spanning forest. This deep connection is especially fruitful to the study of random planar maps. The book is aimed at researchers and graduate students in mathematics and is suitable for a single-semester course; only a basic knowledge of graduate level probability theory is assumed.

Author : Serguei Popov
Publisher : Cambridge University Press
ISBN 13 : 1108472451
Total Pages : 224 pages
Book Rating : 4.56/5 ( download)

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Download or read book Two-Dimensional Random Walk written by Serguei Popov and published by Cambridge University Press. This book was released on 2021-03-18 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: A visual, intuitive introduction in the form of a tour with side-quests, using direct probabilistic insight rather than technical tools.

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.