Download or read book Harmonic Functions and Random Walks on Groups written by Ariel Yadin and published by Cambridge University Press. This book was released on 2024-05-31 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern introduction into the emerging research field of harmonic functions and random walks on groups.

Download or read book Harmonic Functions and Random Walks on Groups written by Ariel Yadin and published by Cambridge University Press. This book was released on 2024-05-31 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research in recent years has highlighted the deep connections between the algebraic, geometric, and analytic structures of a discrete group. New methods and ideas have resulted in an exciting field, with many opportunities for new researchers. This book is an introduction to the area from a modern vantage point. It incorporates the main basics, such as Kesten's amenability criterion, Coulhon and Saloff-Coste inequality, random walk entropy and bounded harmonic functions, the Choquet–Deny Theorem, the Milnor–Wolf Theorem, and a complete proof of Gromov's Theorem on polynomial growth groups. The book is especially appropriate for young researchers, and those new to the field, accessible even to graduate students. An abundance of examples, exercises, and solutions encourage self-reflection and the internalization of the concepts introduced. The author also points to open problems and possibilities for further research.

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.

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.

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.

Download or read book Handbook of Dynamical Systems written by B. Fiedler and published by Gulf Professional Publishing. This book was released on 2002-02-21 with total page 1099 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others. While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to namejust a few, are ubiquitous dynamical concepts throughout the articles.

Download or read book Probability Theory and Mathematical Statistics Vol 2 written by B. Grigelionis and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-18 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "PROB. TH. MATH. ST. ( GRIGELIONIS) VOL. 2 PROC.5/1989 E-BOOK".

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 319 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.

Download or read book Groups Graphs and Random Walks written by Tullio Ceccherini-Silberstein and published by Cambridge University Press. This book was released on 2017-06-29 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date, panoramic account of the theory of random walks on groups and graphs, outlining connections with various mathematical fields.

Download or read book Random Walks Boundaries and Spectra written by Daniel Lenz and published by Springer Science & Business Media. This book was released on 2011-06-16 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings represent the current state of research on the topics 'boundary theory' and 'spectral and probability theory' of random walks on infinite graphs. They are the result of the two workshops held in Styria (Graz and St. Kathrein am Offenegg, Austria) between June 29th and July 5th, 2009. Many of the participants joined both meetings. Even though the perspectives range from very different fields of mathematics, they all contribute with important results to the same wonderful topic from structure theory, which, by extending a quotation of Laurent Saloff-Coste, could be described by 'exploration of groups by random processes'.

Download or read book Positive Harmonic Functions and Diffusion written by Ross G. Pinsky and published by Cambridge University Press. This book was released on 1995-01-12 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Professor Pinsky gives a self-contained account of the theory of positive harmonic functions for second order elliptic operators, using an integrated probabilistic and analytic approach. The book begins with a treatment of the construction and basic properties of diffusion processes. This theory then serves as a vehicle for studying positive harmonic funtions. Starting with a rigorous treatment of the spectral theory of elliptic operators with nice coefficients on smooth, bounded domains, the author then develops the theory of the generalized principal eigenvalue, and the related criticality theory for elliptic operators on arbitrary domains. Martin boundary theory is considered, and the Martin boundary is explicitly calculated for several classes of operators. The book provides an array of criteria for determining whether a diffusion process is transient or recurrent. Also introduced are the theory of bounded harmonic functions, and Brownian motion on manifolds of negative curvature. Many results that form the folklore of the subject are here given a rigorous exposition, making this book a useful reference for the specialist, and an excellent guide for the graduate student.

Download or read book Random Walks Harmonic Functions and Ends of Graphs written by Massimo A. Picardello and published by . This book was released on 1986 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Course on Tug of War Games with Random Noise written by Marta Lewicka and published by Springer Nature. This book was released on 2020-06-19 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate textbook provides a detailed introduction to the probabilistic interpretation of nonlinear potential theory, relying on the recently introduced notion of tug-of-war games with noise. The book explores both basic and more advanced constructions, carefully explaining the parallel between linear and nonlinear cases. The presentation is self-contained with many exercises, making the book suitable as a textbook for a graduate course, as well as for self-study. Extensive background and auxiliary material allow the tailoring of courses to individual student levels.

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.

Download or read book Harmonic Functions on Trees and Buildings written by Adam Korǹyi (et al.) and published by American Mathematical Soc.. This book was released on 1997 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of the workshop "Harmonic Functions on Graphs" held at the Graduate Centre of CUNY in the autumn of 1995. The main papers present material from four minicourses given by leading experts: D. Cartwright, A. Figà-Talamanca, S. Sawyer, and T. Steger. These minicrouses are introductions which gradually progress to deeper and less known branches of the subject. One of the topics treated is buildings, which are discrete analogues of symmetric spaces of arbitrary rank; buildings of rank are trees. Harmonic analysis on buildings is a fairly new and important field of research. One of the minicourses discusses buildings from the combinatorial perspective and another examines them from the p-adic perspective. the third minicourse deals with the connections of trees with p-adic analysis, and the fourth deals with random walks, ie., with the probabilistic side of harmonic functions on trees. The book also contains the extended abstracts of 19 of the 20 lectures given by the participants on their recent results. These abstracts, well detailed and clearly understandable, give a good cross-section of the present state of research in the field.

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.

Download or read book The Bellman Function Technique in Harmonic Analysis written by Vasily Vasyunin and published by Cambridge University Press. This book was released on 2020-08-06 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive reference on the Bellman function method and its applications to various topics in probability and harmonic analysis.