Interacting Particle Systems / Edition 1

Interacting Particle Systems / Edition 1

by Thomas M. Liggett
     
 

ISBN-10: 3540226176

ISBN-13: 9783540226178

Pub. Date: 12/22/2004

Publisher: Springer Berlin Heidelberg

From the reviews

"[...] This book presents a complete treatment of a new class of random processes, which have been studied intensively during the last fifteen years. None of this material has ever appeared in book form before. …The high quality of this work, on a technically difficult subject, makes a fascinating subject and its open problem as accessible

Overview

From the reviews

"[...] This book presents a complete treatment of a new class of random processes, which have been studied intensively during the last fifteen years. None of this material has ever appeared in book form before. …The high quality of this work, on a technically difficult subject, makes a fascinating subject and its open problem as accessible as possible. [...]F.L. Spitzer in Mathematical Reviews, 1986

" [...] This book, the first monographic presentation of this important and rapidly developing theory, will prove indispensable to every serious student of shastics [...]" S. Gacsályi in Publicationes Mathematicae, 1986

"[...] However, it can be said that the author has succeeded in what even experts are seldom able to achieve: To write a clearcut and inspiring book on his favorite subject which meets most, if not all requirements which can be imposed on a comprehensive text on an important new field. The author can be congratulated on his excellent presentation of the theory of interacting particle systems. The book is highly recommended to everyone who works on or is interested in this subject: to probabilists, physicists and theoretical biologists. [...]"
G. Rosenkranz in Methods of Information in Medicine, 1986

Product Details

ISBN-13:
9783540226178
Publisher:
Springer Berlin Heidelberg
Publication date:
12/22/2004
Series:
Classics in Mathematics Series
Edition description:
Reprint of the 1st ed. Berlin Heidelberg New York 1985
Pages:
496
Product dimensions:
9.21(w) x 6.14(h) x 1.04(d)

Table of Contents

Frequently Used Notationxv
Introduction1
Chapter IThe Construction, and Other General Results6
1Markov Processes and Their Semigroups7
2Semigroups and Their Generators12
3The Construction of Generators for Particle Systems20
4Applications of the Construction30
5The Martingale Problem42
6The Martingale Problem for Particle Systems47
7Examples53
8Notes and References61
9Open Problems62
Chapter IISome Basic Tools64
1Coupling64
2Monotonicity and Positive Correlations70
3Duality84
4Relative Entropy88
5Reversibility90
6Recurrence and Transience of Reversible Markov Chains98
7Superpositions of Commuting Markov Chains106
8Perturbations of Random Walks109
9Notes and References119
Chapter IIISpin Systems122
1Couplings for Spin Systems124
2Attractive Spin Systems134
3Attractive Nearest-Neighbor Spin Systems on Z[superscript 1]144
4Duality for Spin Systems157
5Applications of Duality163
6Additive Spin Systems and the Graphical Representation172
7Notes and References175
8Open Problems176
Chapter IVStochastic Ising Models179
1Gibbs States180
2Reversibility of Stochastic Ising Models190
3Phase Transition196
4L[subscript 2] Theory205
5Characterization of Invariant Measures213
6Notes and References222
7Open Problems224
Chapter VThe Voter Model226
1Ergodic Theorems227
2Properties of the Invariant Measures239
3Clustering in One Dimension246
4The Finite System254
5Notes and References262
Chapter VIThe Contact Process264
1The Critical Value265
2Convergence Theorems276
3Rates of Convergence290
4Higher Dimensions307
5Notes and References310
6Open Problems312
Chapter VIINearest-Particle Systems315
1Reversible Finite Systems317
2General Finite Systems325
3Construction of Infinite Systems330
4Reversible Infinite Systems335
5General Infinite Systems347
6Notes and References353
7Open Problems354
Chapter VIIIThe Exclusion Process361
1Ergodic Theorems for Symmetric Systems363
2Coupling and Invariant Measures for General Systems380
3Ergodic Theorems for Translation Invariant Systems384
4The Tagged Particle Process395
5Nonequilibrium Behavior402
6Notes and References413
7Open Problems415
Chapter IXLinear Systems with Values in [0, [infinity])[superscript S]417
1The Construction; Coupling and Duality422
2Survival and Extinction432
3Survival via Second Moments442
4Extinction in One and Two Dimensions449
5Extinction in Higher Dimensions455
6Examples and Applications458
7Notes and References466
8Open Problems467
Bibliography470
Index487
Postface489
Errata495

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >