Random Walks, Boundaries and Spectra
Author: Daniel Lenz
Publisher:
Published: 2011-09-02
Total Pages: 352
ISBN-13: 9783034602471
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Random Walks, Boundaries and Spectra
Author: Daniel Lenz
Publisher: Birkhäuser
Published: 2011-05-08
Total Pages: 326
ISBN-13: 9783034602433
DOWNLOAD EBOOK →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'.
Random Walks, Boundaries and Spectra
Author: Daniel Lenz
Publisher: Springer Science & Business Media
Published: 2011-06-16
Total Pages: 345
ISBN-13: 3034602448
DOWNLOAD EBOOK →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'.
Random Walks on Infinite Graphs and Groups
Author: Wolfgang Woess
Publisher: Cambridge University Press
Published: 2000-02-13
Total Pages: 350
ISBN-13: 0521552923
DOWNLOAD EBOOK →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.
Random Walks and Discrete Potential Theory
Author: M. Picardello
Publisher: Cambridge University Press
Published: 1999-11-18
Total Pages: 378
ISBN-13: 9780521773126
DOWNLOAD EBOOK →Comprehensive and interdisciplinary text covering the interplay between random walks and structure theory.
Elements of the Random Walk
Author: Joseph Rudnick
Publisher: Cambridge University Press
Published: 2004-03-04
Total Pages: 350
ISBN-13: 9781139450140
DOWNLOAD EBOOK →Random walks have proven to be a useful model in understanding processes across a wide spectrum of scientific disciplines. Elements of the Random Walk is an introduction to some of the most powerful and general techniques used in the application of these ideas. The mathematical construct that runs through the analysis of the topics covered in this book, unifying the mathematical treatment, is the generating function. Although the reader is introduced to analytical tools, such as path-integrals and field-theoretical formalism, the book is self-contained in that basic concepts are developed and relevant fundamental findings fully discussed. Mathematical background is provided in supplements at the end of each chapter, when appropriate. This text will appeal to graduate students across science, engineering and mathematics who need to understand the applications of random walk techniques, as well as to established researchers.
Random Walks and Spectral Gaps in Linear Groups
Probability on Graphs
Author: Geoffrey Grimmett
Publisher: Cambridge University Press
Published: 2018-01-25
Total Pages: 279
ISBN-13: 1108542999
DOWNLOAD EBOOK →This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.
Handbook of Dynamical Systems
Author: B. Fiedler
Publisher: Gulf Professional Publishing
Published: 2002-02-21
Total Pages: 1099
ISBN-13: 0080532845
DOWNLOAD EBOOK →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.
Two-Dimensional Random Walk
Author: Serguei Popov
Publisher: Cambridge University Press
Published: 2021-03-18
Total Pages: 224
ISBN-13: 1108472451
DOWNLOAD EBOOK →A visual, intuitive introduction in the form of a tour with side-quests, using direct probabilistic insight rather than technical tools.
