The Self Avoiding Walk

Author : Neal Madras
Publisher : Springer Science & Business Media
ISBN 13 : 1461241324
Total Pages : 433 pages
Book Rating : 4.24/5 ( download)

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Download or read book The Self-Avoiding Walk written by Neal Madras and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-avoiding walk is a path on a lattice that does not visit the same site more than once. In spite of this simple definition, many of the most basic questions about this model are difficult to resolve in a mathematically rigorous fashion. In particular, we do not know much about how far an n step self-avoiding walk typically travels from its starting point, or even how many such walks there are. These and other important questions about the self-avoiding walk remain unsolved in the rigorous mathematical sense, although the physics and chemistry communities have reached consensus on the answers by a variety of nonrigorous methods, including computer simulations. But there has been progress among mathematicians as well, much of it in the last decade, and the primary goal of this book is to give an account of the current state of the art as far as rigorous results are concerned. A second goal of this book is to discuss some of the applications of the self-avoiding walk in physics and chemistry, and to describe some of the nonrigorous methods used in those fields. The model originated in chem istry several decades ago as a model for long-chain polymer molecules. Since then it has become an important model in statistical physics, as it exhibits critical behaviour analogous to that occurring in the Ising model and related systems such as percolation.

Author : Springer
Publisher :
ISBN 13 : 9781461460268
Total Pages : 444 pages
Book Rating : 4.63/5 ( download)

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Download or read book The Self-Avoiding Walk written by Springer and published by . This book was released on 2012-11-01 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Gregory F. Lawler
Publisher : Springer Science & Business Media
ISBN 13 : 1461459729
Total Pages : 226 pages
Book Rating : 4.29/5 ( download)

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Download or read book Intersections of Random Walks written by Gregory F. Lawler and published by Springer Science & Business Media. This book was released on 2012-11-06 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Christian Lindorfer
Publisher : Springer
ISBN 13 : 3658247649
Total Pages : 65 pages
Book Rating : 4.45/5 ( download)

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Download or read book The Language of Self-Avoiding Walks written by Christian Lindorfer and published by Springer. This book was released on 2019-01-07 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: The connective constant of a quasi-transitive infinite graph is a measure for the asymptotic growth rate of the number of self-avoiding walks of length n from a given starting vertex. On edge-labelled graphs the formal language of self-avoiding walks is generated by a formal grammar, which can be used to calculate the connective constant of the graph. Christian Lindorfer discusses the methods in some examples, including the infinite ladder-graph and the sandwich of two regular infinite trees.

Author : Roberto Fernandez
Publisher : Springer Science & Business Media
ISBN 13 : 3662028662
Total Pages : 446 pages
Book Rating : 4.67/5 ( download)

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Download or read book Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory written by Roberto Fernandez and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simple random walks - or equivalently, sums of independent random vari ables - have long been a standard topic of probability theory and mathemat ical physics. In the 1950s, non-Markovian random-walk models, such as the self-avoiding walk,were introduced into theoretical polymer physics, and gradu ally came to serve as a paradigm for the general theory of critical phenomena. In the past decade, random-walk expansions have evolved into an important tool for the rigorous analysis of critical phenomena in classical spin systems and of the continuum limit in quantum field theory. Among the results obtained by random-walk methods are the proof of triviality of the cp4 quantum field theo ryin space-time dimension d (::::) 4, and the proof of mean-field critical behavior for cp4 and Ising models in space dimension d (::::) 4. The principal goal of the present monograph is to present a detailed review of these developments. It is supplemented by a brief excursion to the theory of random surfaces and various applications thereof. This book has grown out of research carried out by the authors mainly from 1982 until the middle of 1985. Our original intention was to write a research paper. However, the writing of such a paper turned out to be a very slow process, partly because of our geographical separation, partly because each of us was involved in other projects that may have appeared more urgent.

Author : Carlo Vanderzande
Publisher : Cambridge University Press
ISBN 13 : 0521559936
Total Pages : 240 pages
Book Rating : 4.35/5 ( download)

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Download or read book Lattice Models of Polymers written by Carlo Vanderzande and published by Cambridge University Press. This book was released on 1998-04-30 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to lattice models of polymers. This is an important topic both in the theory of critical phenomena and the modelling of polymers. The first two chapters introduce the basic theory of random, directed and self-avoiding walks. The next two chapters develop and expand this theory to explore the self-avoiding walk in both two and three dimensions. Following chapters describe polymers near a surface, dense polymers, self-interacting polymers and branched polymers. The book closes with discussions of some geometrical and topological properties of polymers, and of self-avoiding surfaces on a lattice. The volume combines results from rigorous analytical and numerical work to give a coherent picture of the properties of lattice models of polymers. This book will be valuable for graduate students and researchers working in statistical mechanics, theoretical physics and polymer physics. It will also be of interest to those working in applied mathematics and theoretical chemistry.

Author : Roland Bauerschmidt
Publisher : Springer Nature
ISBN 13 : 9813295937
Total Pages : 283 pages
Book Rating : 4.33/5 ( download)

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Download or read book Introduction to a Renormalisation Group Method written by Roland Bauerschmidt and published by Springer Nature. This book was released on 2019-10-16 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a primer on a mathematically rigorous renormalisation group theory, presenting mathematical techniques fundamental to renormalisation group analysis such as Gaussian integration, perturbative renormalisation and the stable manifold theorem. It also provides an overview of fundamental models in statistical mechanics with critical behaviour, including the Ising and φ4 models and the self-avoiding walk. The book begins with critical behaviour and its basic discussion in statistical mechanics models, and subsequently explores perturbative and non-perturbative analysis in the renormalisation group. Lastly it discusses the relation of these topics to the self-avoiding walk and supersymmetry. Including exercises in each chapter to help readers deepen their understanding, it is a valuable resource for mathematicians and mathematical physicists wanting to learn renormalisation group theory.

Author : Geoffrey Grimmett
Publisher : Cambridge University Press
ISBN 13 : 1108542999
Total Pages : 279 pages
Book Rating : 4.99/5 ( download)

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Download or read book Probability on Graphs written by Geoffrey Grimmett and published by Cambridge University Press. This book was released on 2018-01-25 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Michael N. Barber
Publisher : CRC Press
ISBN 13 : 9780677026206
Total Pages : 190 pages
Book Rating : 4.0X/5 ( download)

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Download or read book Random and Restricted Walks written by Michael N. Barber and published by CRC Press. This book was released on 1970 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Vladas Sidoravicius
Publisher : Springer
ISBN 13 : 9789811503047
Total Pages : 0 pages
Book Rating : 4.44/5 ( download)

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Download or read book Sojourns in Probability Theory and Statistical Physics - III written by Vladas Sidoravicius and published by Springer. This book was released on 2020-10-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Charles M. (Chuck) Newman has been a leader in Probability Theory and Statistical Physics for nearly half a century. This three-volume set is a celebration of the far-reaching scientific impact of his work. It consists of articles by Chuck’s collaborators and colleagues across a number of the fields to which he has made contributions of fundamental significance. This publication was conceived during a conference in 2016 at NYU Shanghai that coincided with Chuck's 70th birthday. The sub-titles of the three volumes are: I. Spin Glasses and Statistical Mechanics II. Brownian Web and Percolation III. Interacting Particle Systems and Random Walks The articles in these volumes, which cover a wide spectrum of topics, will be especially useful for graduate students and researchers who seek initiation and inspiration in Probability Theory and Statistical Physics.