Stochastic Interacting Systems: Contact, Voter and Exclusion ProcessesInteractive Particle Systems is a branch of Probability Theory with close connections to Mathematical Physics and Mathematical Biology. In 1985, the author wrote a book (T. Liggett, Interacting Particle System, ISBN 3-540-96069) that treated the subject as it was at that time. The present book takes three of the most important models in the area, and traces advances in our understanding of them since 1985. In so doing, many of the most useful techniques in the field are explained and developed, so that they can be applied to other models and in other contexts. Extensive Notes and References sections discuss other work on these and related models. Readers are expected to be familiar with analysis and probability at the graduate level, but it is not assumed that they have mastered the material in the 1985 book. This book is intended for graduate students and researchers in Probability Theory, and in related areas of Mathematics, Biology and Physics. |
From inside the book
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Contents
I | 1 |
III | 4 |
IV | 5 |
V | 6 |
VI | 8 |
VII | 11 |
VIII | 12 |
IX | 13 |
LXI | 151 |
LXII | 153 |
LXIII | 155 |
LXV | 156 |
LXVI | 158 |
LXVII | 159 |
LXVIII | 162 |
LXIX | 167 |
X | 14 |
XI | 16 |
XII | 21 |
XIII | 22 |
XIV | 25 |
XV | 26 |
XVI | 29 |
XVII | 31 |
XVIII | 32 |
XIX | 34 |
XX | 35 |
XXI | 36 |
XXII | 38 |
XXIII | 40 |
XXIV | 42 |
XXV | 44 |
XXVII | 45 |
XXVIII | 50 |
XXIX | 51 |
XXX | 54 |
XXXI | 57 |
XXXII | 60 |
XXXIII | 69 |
XXXIV | 71 |
XXXV | 72 |
XXXVI | 74 |
XXXVII | 78 |
XXXVIII | 79 |
XXXIX | 80 |
XL | 86 |
XLI | 91 |
XLII | 94 |
XLIII | 96 |
XLIV | 103 |
XLV | 104 |
XLVI | 105 |
XLVII | 109 |
XLVIII | 119 |
XLIX | 123 |
L | 125 |
LI | 139 |
LII | 140 |
LIV | 142 |
LVI | 143 |
LVII | 145 |
LVIII | 146 |
LX | 147 |
LXX | 174 |
LXXI | 180 |
LXXII | 184 |
LXXIII | 185 |
LXXIV | 191 |
LXXV | 201 |
LXXVI | 209 |
LXXVII | 210 |
LXXVIII | 212 |
LXXIX | 215 |
LXXXI | 218 |
LXXXII | 219 |
LXXXIII | 220 |
LXXXV | 222 |
LXXXVI | 224 |
LXXXVII | 225 |
LXXXVIII | 226 |
LXXXIX | 230 |
XC | 232 |
XCI | 234 |
XCII | 238 |
XCIII | 240 |
XCIV | 242 |
XCV | 253 |
XCVI | 258 |
XCVII | 261 |
XCVIII | 262 |
XCIX | 264 |
C | 266 |
CI | 268 |
CII | 269 |
CIII | 272 |
CIV | 273 |
CV | 276 |
CVI | 278 |
CVIII | 280 |
CIX | 284 |
CX | 285 |
CXI | 286 |
CXII | 288 |
CXIII | 290 |
CXIV | 294 |
CXV | 295 |
CXVI | 298 |
CXVII | 317 |
331 | |
Other editions - View all
Stochastic Interacting Systems: Contact, Voter and Exclusion Processes Thomas M. Liggett Limited preview - 2013 |
Stochastic Interacting Systems: Contact, Voter and Exclusion Processes Thomas M. Liggett No preview available - 2014 |
Stochastic Interacting Systems: Contact, Voter and Exclusion Processes Thomas M. Liggett No preview available - 2010 |
Common terms and phrases
A₁ active path analogous argument asymptotic bounded branching random walk central limit theorem compute condition consider construction Corollary corresponding coupling critical value defined density dimensional duality Durrett equation ergodic exclusion process exponential extremal invariant measures fact Ferrari finite function gives graphical representation implies independent inequality infection arrows initial configuration initial distribution integer law of large left side Lemma Liggett linear voter models Markov chain Markov property martingale monotonicity nearest neighbor nonnegative nontrivial invariant measure Note oriented percolation P(en parameter particle systems pivotal interval Poisson processes positive probability measure process on Zd product measure proof of Theorem Proposition proved random walk Recall result right side satisfies Schonmann second class particle Section sequence statement stationary stochastic Suppose survive strongly symmetric Theorem B21 threshold contact process threshold voter model transition translation invariant X₁ zero