Stochastic Interacting Systems: Contact, Voter and Exclusion Processes

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Springer Science & Business Media, Aug 13, 1999 - Education - 332 pages
Interactive 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.

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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
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XXIII
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XXIV
42
XXV
44
XXVII
45
XXVIII
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XXIX
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XXX
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XXXI
57
XXXII
60
XXXIII
69
XXXIV
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XXXV
72
XXXVI
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XXXVII
78
XXXVIII
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XXXIX
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XL
86
XLI
91
XLII
94
XLIII
96
XLIV
103
XLV
104
XLVI
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XLVII
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XLVIII
119
XLIX
123
L
125
LI
139
LII
140
LIV
142
LVI
143
LVII
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LVIII
146
LX
147
LXX
174
LXXI
180
LXXII
184
LXXIII
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LXXIV
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LXXV
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LXXVI
209
LXXVII
210
LXXVIII
212
LXXIX
215
LXXXI
218
LXXXII
219
LXXXIII
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LXXXV
222
LXXXVI
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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
CXVIII
331
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