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Author : M. Picardello,W. Woess
Publisher : Cambridge University Press
Page : 378 pages
File Size : 46,8 Mb
Release : 1999-11-18
Category : Mathematics
ISBN : 0521773121
Comprehensive and interdisciplinary text covering the interplay between random walks and structure theory.
Author : M.A. Picardello
Publisher : Springer Science & Business Media
Page : 299 pages
File Size : 40,6 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781489923233
This book collects the Proceedings of a Congress held in Frascati (Rome) in the period July 1 -July 10, 1991, on the subject of harmonic analysis and discrete potential theory, and related topics. The Congress was made possible by the financial support of the Italian National Research Council ("Gruppo GNAFA"), the Ministry of University ("Gruppo Analisi Funzionale" of the University of Milano), the University of Rome "Tor Vergata", and was also patronized by the Centro "Vito Volterra" of the University of Rome "Tor Vergata". Financial support for publishing these Proceedings was provided by the University of Rome "Tor Vergata", and by a generous contribution of the Centro "Vito Volterra". I am happy of this opportunity to acknowledge the generous support of all these Institutions, and to express my gratitude, and that of all the participants. A number of distinguished mathematicians took part in the Congress. Here is the list of participants: M. Babillot, F. Choucroun, Th. Coulhon, L. Elie, F. Ledrappier, N. Th. Varopoulos (Paris); L. Gallardo (Brest); Ph. Bougerol, B. Roynette (Nancy); O. Gebuhrer (Strasbourg); G. Ahumada-Bustamante (Mulhouse); A. Valette (Neuchatel); P. Gerl (Salzburg); W. Hansen, H. Leptin (Bielefeld); M. Bozejko, A. Hulanicki, T. Pytlik (Wroclaw); C. Thomassen (Lyngby); P. Sjogren (Goteborg); V. Kaimanovich (Leningrad); A. Nevo (Jerusalem); T. Steger (Chicago); S. Sawyer, M. Taibleson, G. Weiss (St. Louis); J. Cohen, S.S ali ani (Maryland); D. Voiculescu (Berkeley); A. Zemanian (Stony Brook); S. Northshield (Plattsburgh); J. Taylor (Montreal); J
Author : Takashi Kumagai
Publisher : Springer
Page : 147 pages
File Size : 53,8 Mb
Release : 2014-01-25
Category : Mathematics
ISBN : 9783319031521
In these lecture notes, we will analyze the behavior of random walk on disordered media by means of both probabilistic and analytic methods, and will study the scaling limits. We will focus on the discrete potential theory and how the theory is effectively used in the analysis of disordered media. The first few chapters of the notes can be used as an introduction to discrete potential theory. Recently, there has been significant progress on the theory of random walk on disordered media such as fractals and random media. Random walk on a percolation cluster(‘the ant in the labyrinth’)is one of the typical examples. In 1986, H. Kesten showed the anomalous behavior of a random walk on a percolation cluster at critical probability. Partly motivated by this work, analysis and diffusion processes on fractals have been developed since the late eighties. As a result, various new methods have been produced to estimate heat kernels on disordered media. These developments are summarized in the notes.
Author : Frank Spitzer
Publisher : Springer Science & Business Media
Page : 419 pages
File Size : 47,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475742299
This book is devoted exclusively to a very special class of random processes, namely, to random walk on the lattice points of ordinary Euclidian space. The author considers this high degree of specialization worthwhile because the theory of such random walks is far more complete than that of any larger class of Markov chains. Almost 100 pages of examples and problems are included.
Author : Wolfgang Woess
Publisher : Cambridge University Press
Page : 350 pages
File Size : 42,9 Mb
Release : 2000-02-13
Category : Mathematics
ISBN : 9780521552929
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 : Andras Telcs
Publisher : Springer
Page : 200 pages
File Size : 50,6 Mb
Release : 2006-10-18
Category : Mathematics
ISBN : 9783540330288
The main aim of this book is to reveal connections between the physical and geometric properties of space and diffusion. This is done in the context of random walks in the absence of algebraic structure, local or global spatial symmetry or self-similarity. The author studies heat diffusion at this general level and discusses the multiplicative Einstein relation; Isoperimetric inequalities; and Heat kernel estimates; Elliptic and parabolic Harnack inequality.
Author : Vadim Kaimanovich
Publisher : Walter de Gruyter
Page : 545 pages
File Size : 52,5 Mb
Release : 2008-08-22
Category : Mathematics
ISBN : 9783110198089
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 : Harry Kesten
Publisher : Springer Science & Business Media
Page : 358 pages
File Size : 55,6 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662094440
Most probability problems involve random variables indexed by space and/or time. These problems almost always have a version in which space and/or time are taken to be discrete. This volume deals with areas in which the discrete version is more natural than the continuous one, perhaps even the only one than can be formulated without complicated constructions and machinery. The 5 papers of this volume discuss problems in which there has been significant progress in the last few years; they are motivated by, or have been developed in parallel with, statistical physics. They include questions about asymptotic shape for stochastic growth models and for random clusters; existence, location and properties of phase transitions; speed of convergence to equilibrium in Markov chains, and in particular for Markov chains based on models with a phase transition; cut-off phenomena for random walks. The articles can be read independently of each other. Their unifying theme is that of models built on discrete spaces or graphs. Such models are often easy to formulate. Correspondingly, the book requires comparatively little previous knowledge of the machinery of probability.
Author : Daniel Lenz,Florian Sobieczky,Wolfgang Woess
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 53,8 Mb
Release : 2011-06-16
Category : Mathematics
ISBN : 9783034602440
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'.
Author : Motoko Kotani
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 47,5 Mb
Release : 2004
Category : Geometry, Differential
ISBN : 9780821833513
This book is a collection of papers from the proceedings of the first symposium of the Japan Association for Mathematical Sciences. Topics covered center around problems of geometric analysis in relation to heat kernels, random walks, and Poisson boundaries on discrete groups, graphs, and other combinatorial objects. The material is suitable for graduate students and research mathematicians interested in heat kernels and random works on groups and graphs.
Author : M. T. Barlow
Publisher : Cambridge University Press
Page : 239 pages
File Size : 43,8 Mb
Release : 2017-02-23
Category : Mathematics
ISBN : 9781107674424
Useful but hard-to-find results enrich this introduction to the analytic study of random walks on infinite graphs.
Author : Masanori Kishi
Publisher : Walter de Gruyter
Page : 417 pages
File Size : 43,8 Mb
Release : 2011-05-02
Category : Mathematics
ISBN : 9783110859065
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Author : Philippe Biane,Luc Bouten,Fabio Cipriani,Norio Konno,Quanhua Xu
Publisher : Springer
Page : 464 pages
File Size : 41,9 Mb
Release : 2008-10-16
Category : Mathematics
ISBN : 9783540693659
This book offers the revised and completed notes of lectures given at the 2007 conference, "Quantum Potential Theory: Structures and Applications to Physics." These lectures provide an introduction to the theory and discuss various applications.
Author : Alexander Grigor'yan,Yuhua Sun
Publisher : Walter de Gruyter GmbH & Co KG
Page : 526 pages
File Size : 46,6 Mb
Release : 2021-01-18
Category : Mathematics
ISBN : 9783110700763
The book covers the latest research in the areas of mathematics that deal the properties of partial differential equations and stochastic processes on spaces in connection with the geometry of the underlying space. Written by experts in the field, this book is a valuable tool for the advanced mathematician.
Author : Josef Kral,Jaroslav Lukes,Ivan Netuka,Jiri Vesely
Publisher : Walter de Gruyter
Page : 513 pages
File Size : 47,8 Mb
Release : 2011-10-13
Category : Mathematics
ISBN : 9783110818574
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.