Random Walks And Discrete Potential Theory
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Author |
: M. Picardello |
Publisher |
: Cambridge University Press |
Total Pages |
: 378 |
Release |
: 1999-11-18 |
ISBN-10 |
: 0521773121 |
ISBN-13 |
: 9780521773126 |
Rating |
: 4/5 (21 Downloads) |
Synopsis Random Walks and Discrete Potential Theory by : M. Picardello
Comprehensive and interdisciplinary text covering the interplay between random walks and structure theory.
Author |
: Takashi Kumagai |
Publisher |
: Springer |
Total Pages |
: 155 |
Release |
: 2014-01-25 |
ISBN-10 |
: 9783319031521 |
ISBN-13 |
: 331903152X |
Rating |
: 4/5 (21 Downloads) |
Synopsis Random Walks on Disordered Media and their Scaling Limits by : Takashi Kumagai
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 |
: Massimo Picardello |
Publisher |
: |
Total Pages |
: |
Release |
: 1999 |
ISBN-10 |
: OCLC:652420945 |
ISBN-13 |
: |
Rating |
: 4/5 (45 Downloads) |
Synopsis Random Walks and Discrete Potential Theory. Cortona 1997 by : Massimo Picardello
Author |
: M.A. Picardello |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 299 |
Release |
: 2013-11-11 |
ISBN-10 |
: 9781489923233 |
ISBN-13 |
: 1489923233 |
Rating |
: 4/5 (33 Downloads) |
Synopsis Harmonic Analysis and Discrete Potential Theory by : M.A. Picardello
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 |
Total Pages |
: 419 |
Release |
: 2013-03-14 |
ISBN-10 |
: 9781475742299 |
ISBN-13 |
: 1475742290 |
Rating |
: 4/5 (99 Downloads) |
Synopsis Principles of Random Walk by : Frank Spitzer
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 |
Total Pages |
: 193 |
Release |
: 2006-10-18 |
ISBN-10 |
: 9783540330288 |
ISBN-13 |
: 3540330283 |
Rating |
: 4/5 (88 Downloads) |
Synopsis The Art of Random Walks by : Andras Telcs
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 |
Total Pages |
: 224 |
Release |
: 2021-03-18 |
ISBN-10 |
: 9781108472456 |
ISBN-13 |
: 1108472451 |
Rating |
: 4/5 (56 Downloads) |
Synopsis Two-Dimensional Random Walk by : Serguei Popov
A visual, intuitive introduction in the form of a tour with side-quests, using direct probabilistic insight rather than technical tools.
Author |
: Steven P. Lalley |
Publisher |
: Springer Nature |
Total Pages |
: 373 |
Release |
: 2023-05-08 |
ISBN-10 |
: 9783031256325 |
ISBN-13 |
: 3031256328 |
Rating |
: 4/5 (25 Downloads) |
Synopsis Random Walks on Infinite Groups by : Steven P. Lalley
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 |
: Wolfgang Woess |
Publisher |
: Cambridge University Press |
Total Pages |
: 350 |
Release |
: 2000-02-13 |
ISBN-10 |
: 9780521552929 |
ISBN-13 |
: 0521552923 |
Rating |
: 4/5 (29 Downloads) |
Synopsis Random Walks on Infinite Graphs and Groups by : Wolfgang Woess
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 |
: Daniel Lenz |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 345 |
Release |
: 2011-06-16 |
ISBN-10 |
: 9783034602440 |
ISBN-13 |
: 3034602448 |
Rating |
: 4/5 (40 Downloads) |
Synopsis Random Walks, Boundaries and Spectra by : Daniel Lenz
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'.