Description: Probability on Discrete Structures by Harry Kesten, David Aldous, Geoffrey R. Grimmett, C. Douglas Howard, Fabio Martinelli, J. Michael Steele, Laurent Saloff-Coste Most probability problems involve random variables indexed by space and/or time. speed of convergence to equilibrium in Markov chains, and in particular for Markov chains based on models with a phase transition; Their unifying theme is that of models built on discrete spaces or graphs. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description 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. Back Cover 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. Table of Contents The Objective Method: Probabilistic Combinatorial Optimization and Local Weak Convergence.- The Random-Cluster Model.- Models of First-Passage Percolation.- Relaxation Times of Markov Chains in Statistical Mechanics and Combinatorial Structures.- Random Walks on Finite Groups. Review From the reviews:"The ... book contains five survey articles which span a very nice part of modern discrete probability theory. … The world of discrete probability theory seems to be growing at an exponential rate and it is exactly for this reason that such surveys are not only welcome but essential. Each one of these articles is indeed very interesting and both the beginner … and the expert can learn a tremendous amount. In short, it is a wonderful book and to be recommended." (Jeffrey E. Steif, Combinatorics, Probability and Computing, Vol. 14, 2005) "This book covers probability problems with random variables whose indices take discrete values. The exposition is very clear and the book provides an introduction to the subject and to the mathematical formalism which is used. Each chapter is on a different topic, and it represents a clear, rather complete review of the state of the art of its own subject." (Guido Gentile, SIAM Review, Vol. 47 (3), 2005) Long Description 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. Review Quote From the reviews:"The ... book contains five survey articles which span a very nice part of modern discrete probability theory. … The world of discrete probability theory seems to be growing at an exponential rate and it is exactly for this reason that such surveys are not only welcome but essential. Each one of these articles is indeed very interesting and both the beginner … and the expert can learn a tremendous amount. In short, it is a wonderful book and to be recommended." (Jeffrey E. Steif, Combinatorics, Probability and Computing, Vol. 14, 2005) "This book covers probability problems with random variables whose indices take discrete values. The exposition is very clear and the book provides an introduction to the subject and to the mathematical formalism which is used. Each chapter is on a different topic, and it represents a clear, rather complete review of the state of the art of its own subject." (Guido Gentile, SIAM Review, Vol. 47 (3), 2005) Feature 1st volume of a new probability subseries of EMS under the editorship of A.-S. Sznitman (ETH Zurich) and S.R.S. Varadhan (NYU) Written by outstanding probabilists who are professors at well-known universities in the US and Europe Details ISBN3540008454 Author Laurent Saloff-Coste Short Title PROBABILITY ON DISCRETE STRUCT Series Encyclopaedia of Mathematical Sciences Language English ISBN-10 3540008454 ISBN-13 9783540008453 Media Book Format Hardcover DEWEY 519.2 Series Number 110 Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K Place of Publication Berlin Country of Publication Germany Edited by Harry Kesten Pages 351 Edition 2004th DOI 10.1007/b11071 Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Edition Description 2004 ed. Year 2003 Publication Date 2003-09-18 Alternative 9783642056475 Illustrations IX, 351 p. Audience General We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96277619;
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ISBN-13: 9783540008453
Book Title: Probability on Discrete Structures
Number of Pages: 351 Pages
Language: English
Publication Name: Probability on Discrete Structures
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg, J. Michael Steele, Laurent Saloff-Coste, Fabio Martinelli, Geoffrey R. Grimmett, C. Douglas Howard, David Aldous
Publication Year: 2003
Subject: Mathematics
Item Height: 235 mm
Item Weight: 1510 g
Type: Textbook
Author: Harry Kesten
Item Width: 155 mm
Format: Hardcover
