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Author : M. Picardello
Publisher : Cambridge University Press
Page : 378 pages
File Size : 20,14 MB
Release : 1999-11-18
Category : Mathematics
ISBN : 9780521773126
Comprehensive and interdisciplinary text covering the interplay between random walks and structure theory.
Author : Massimo Picardello
Publisher :
Page : pages
File Size : 38,37 MB
Release : 1999
Category :
ISBN :
Author : Takashi Kumagai
Publisher : Springer
Page : 155 pages
File Size : 13,39 MB
Release : 2014-01-25
Category : Mathematics
ISBN : 331903152X
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 : M.A. Picardello
Publisher : Springer Science & Business Media
Page : 299 pages
File Size : 39,4 MB
Release : 2013-11-11
Category : Mathematics
ISBN : 1489923233
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 : Frank Spitzer
Publisher : Springer Science & Business Media
Page : 419 pages
File Size : 34,95 MB
Release : 2013-03-14
Category : Mathematics
ISBN : 1475742290
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 : Andras Telcs
Publisher : Springer
Page : 193 pages
File Size : 14,96 MB
Release : 2006-10-18
Category : Mathematics
ISBN : 3540330283
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 : Serguei Popov
Publisher : Cambridge University Press
Page : 224 pages
File Size : 46,21 MB
Release : 2021-03-18
Category : Mathematics
ISBN : 1108472451
A visual, intuitive introduction in the form of a tour with side-quests, using direct probabilistic insight rather than technical tools.
Author : Wolfgang Woess
Publisher : Cambridge University Press
Page : 350 pages
File Size : 41,25 MB
Release : 2000-02-13
Category : Mathematics
ISBN : 0521552923
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 : M. T. Barlow
Publisher : Cambridge University Press
Page : 239 pages
File Size : 29,23 MB
Release : 2017-02-23
Category : Mathematics
ISBN : 1107674425
Useful but hard-to-find results enrich this introduction to the analytic study of random walks on infinite graphs.
Author : Yves Le Jan
Publisher : Springer
Page : 0 pages
File Size : 50,89 MB
Release : 2024-07-27
Category : Mathematics
ISBN : 9783031579226
This book presents fundamental relations between random walks on graphs and field theories of mathematical physics. Such relations have been explored for several decades and remain a rapidly developing research area in probability theory. The main objects of study include Markov loops, spanning forests, random holonomies, and covers, and the purpose of the book is to investigate their relations to Bose fields, Fermi fields, and gauge fields. The book starts with a review of some basic notions of Markovian potential theory in the simple context of a finite or countable graph, followed by several chapters dedicated to the study of loop ensembles and related statistical physical models. Then, spanning trees and Fermi fields are introduced and related to loop ensembles. Next, the focus turns to topological properties of loops and graphs, with the introduction of connections on a graph, loop holonomies, and Yang–Mills measure. Among the main results presented is an intertwining relation between merge-and-split generators on loop ensembles and Casimir operators on connections, and the key reflection positivity property for the fields under consideration. Aimed at researchers and graduate students in probability and mathematical physics, this concise monograph is essentially self-contained. Familiarity with basic notions of probability, Poisson point processes, and discrete Markov chains are assumed of the reader.