Random Walk Intersections
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Intersections Of Random Walks
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Author : Gregory F. Lawler
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Intersections Of Random Walks written by Gregory F. Lawler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
A more accurate title for this book would be "Problems dealing with the non-intersection of paths of random walks. " These include: harmonic measure, which can be considered as a problem of nonintersection of a random walk with a fixed set; the probability that the paths of independent random walks do not intersect; and self-avoiding walks, i. e. , random walks which have no self-intersections. The prerequisite is a standard measure theoretic course in probability including martingales and Brownian motion. The first chapter develops the facts about simple random walk that will be needed. The discussion is self-contained although some previous expo sure to random walks would be helpful. Many of the results are standard, and I have made borrowed from a number of sources, especially the ex cellent book of Spitzer [65]. For the sake of simplicity I have restricted the discussion to simple random walk. Of course, many of the results hold equally well for more general walks. For example, the local central limit theorem can be proved for any random walk whose increments have mean zero and finite variance. Some of the later results, especially in Section 1. 7, have not been proved for very general classes of walks. The proofs here rely heavily on the fact that the increments of simple random walk are bounded and symmetric.
Random Walk Intersections
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Author : Xia Chen
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Random Walk Intersections written by Xia Chen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
Involves important and non-trivial results in contemporary probability theory motivated by polymer models, as well as other topics of importance in physics and chemistry.
Intersections Of Random Walks
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Author : Gregoyr Lawler
language : en
Publisher: Birkhäuser
Release Date : 2012-07-02
Intersections Of Random Walks written by Gregoyr Lawler and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-02 with Mathematics categories.
A more accurate title for this book would be "Problems dealing with the non-intersection of paths of random walks. " These include: harmonic measure, which can be considered as a problem of nonintersection of a random walk with a fixed set; the probability that the paths of independent random walks do not intersect; and self-avoiding walks, i. e. , random walks which have no self-intersections. The prerequisite is a standard measure theoretic course in probability including martingales and Brownian motion. The first chapter develops the facts about simple random walk that will be needed. The discussion is self-contained although some previous expo sure to random walks would be helpful. Many of the results are standard, and I have made borrowed from a number of sources, especially the ex cellent book of Spitzer [65]. For the sake of simplicity I have restricted the discussion to simple random walk. Of course, many of the results hold equally well for more general walks. For example, the local central limit theorem can be proved for any random walk whose increments have mean zero and finite variance. Some of the later results, especially in Section 1. 7, have not been proved for very general classes of walks. The proofs here rely heavily on the fact that the increments of simple random walk are bounded and symmetric.
Intersection Exponents For Random Walks On Cylinders
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Author : Brigitta Karola Vermesi
language : en
Publisher:
Release Date : 2006
Intersection Exponents For Random Walks On Cylinders written by Brigitta Karola Vermesi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
Intersections Of Random Walks
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Author : Gregory F. Lawler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-06
Intersections Of Random Walks written by Gregory F. Lawler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-06 with Mathematics categories.
A central study in Probability Theory is the behavior of fluctuation phenomena of partial sums of different types of random variable. One of the most useful concepts for this purpose is that of the random walk which has applications in many areas, particularly in statistical physics and statistical chemistry. Originally published in 1991, Intersections of Random Walks focuses on and explores a number of problems dealing primarily with the nonintersection of random walks and the self-avoiding walk. Many of these problems arise in studying statistical physics and other critical phenomena. Topics include: discrete harmonic measure, including an introduction to diffusion limited aggregation (DLA); the probability that independent random walks do not intersect; and properties of walks without self-intersections. The present softcover reprint includes corrections and addenda from the 1996 printing, and makes this classic monograph available to a wider audience. With a self-contained introduction to the properties of simple random walks, and an emphasis on rigorous results, the book will be useful to researchers in probability and statistical physics and to graduate students interested in basic properties of random walks.
Random Walk A Modern Introduction
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Author : Gregory F. Lawler
language : en
Publisher: Cambridge University Press
Release Date : 2010-06-24
Random Walk A Modern Introduction written by Gregory F. Lawler and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-24 with Mathematics categories.
Random walks are stochastic processes formed by successive summation of independent, identically distributed random variables and are one of the most studied topics in probability theory. This contemporary introduction evolved from courses taught at Cornell University and the University of Chicago by the first author, who is one of the most highly regarded researchers in the field of stochastic processes. This text meets the need for a modern reference to the detailed properties of an important class of random walks on the integer lattice. It is suitable for probabilists, mathematicians working in related fields, and for researchers in other disciplines who use random walks in modeling.
Moderate Deviations For The Range Of Planar Random Walks
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Author : Richard F. Bass
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-03-06
Moderate Deviations For The Range Of Planar Random Walks written by Richard F. Bass and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-06 with Mathematics categories.
Given a symmetric random walk in ${\mathbb Z}^2$ with finite second moments, let $R_n$ be the range of the random walk up to time $n$. The authors study moderate deviations for $R_n -{\mathbb E}R_n$ and ${\mathbb E}R_n -R_n$. They also derive the corresponding laws of the iterated logarithm.
Random Walk A Modern Introduction
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Author : Gregory F. Lawler
language : en
Publisher: Cambridge University Press
Release Date : 2010-06-24
Random Walk A Modern Introduction written by Gregory F. Lawler and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-24 with Mathematics categories.
Random walks are stochastic processes formed by successive summation of independent, identically distributed random variables and are one of the most studied topics in probability theory. This contemporary introduction evolved from courses taught at Cornell University and the University of Chicago by the first author, who is one of the most highly regarded researchers in the field of stochastic processes. This text meets the need for a modern reference to the detailed properties of an important class of random walks on the integer lattice. It is suitable for probabilists, mathematicians working in related fields, and for researchers in other disciplines who use random walks in modeling.
Mathematics Of Random Media
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Author : Werner E. Kohler
language : en
Publisher: American Mathematical Soc.
Release Date :
Mathematics Of Random Media written by Werner E. Kohler and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
In recent years, there has been remarkable growth in the mathematics of random media. The field has deep scientific and technological roots, as well as purely mathematical ones in the theory of stochastic processes. This collection of papers by leading researchers provides an overview of this rapidly developing field. The papers were presented at the 1989 AMS-SIAM Summer Seminar in Applied Mathematics, held at Virginia Polytechnic Institute and State University in Blacksburg, Virginia. In addition to new results on stochastic differential equations and Markov processes, fields whose elegant mathematical techniques are of continuing value in application areas, the conference was organized around four themes: Systems of interacting particles are normally viewed in connection with the fundamental problems of statistical mechanics, but have also been used to model diverse phenomena such as computer architectures and the spread of biological populations. Powerful mathematical techniques have been developed for their analysis, and a number of important systems are now well understood. Random perturbations of dynamical systems have also been used extensively as models in physics, chemistry, biology, and engineering. Among the recent unifying mathematical developments is the theory of large deviations, which enables the accurate calculation of the probabilities of rare events. For these problems, approaches based on effective but formal perturbation techniques parallel rigorous mathematical approaches from probability theory and partial differential equations. The book includes representative papers from forefront research of both types. Effective medium theory, otherwise known as the mathematical theory of homogenization, consists of techniques for predicting the macroscopic properties of materials from an understanding of their microstructures. For example, this theory is fundamental in the science of composites, where it is used for theoretical determination of electrical and mechanical properties. Furthermore, the inverse problem is potentially of great technological importance in the design of composite materials which have been optimized for some specific use. Mathematical theories of the propagation of waves in random media have been used to understand phenomena as diverse as the twinkling of stars, the corruption of data in geophysical exploration, and the quantum mechanics of disordered solids. Especially effective methods now exist for waves in randomly stratified, one-dimensional media. A unifying theme is the mathematical phenomenon of localization, which occurs when a wave propogating into a random medium is attenuated exponentially with propagation distance, with the attenuation caused solely by the mechanism of random multiple scattering. Because of the wide applicability of this field of research, this book would appeal to mathematicians, scientists, and engineers in a wide variety of areas, including probabilistic methods, the theory of disordered materials, systems of interacting particles, the design of materials, and dynamical systems driven by noise. In addition, graduate students and others will find this book useful as an overview of current research in random media.
Random Walks
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Author : Pál Révész
language : en
Publisher: Janos Bolyai Mathematical Society
Release Date : 1999
Random Walks written by Pál Révész and has been published by Janos Bolyai Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.