Probability on graphs: random processes on graphs and lattices
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2010
|
| Edition: | 1. publ. |
| Series: | Textbooks / Institute of Mathematical Statistics
1 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XI, 247 S. graph. Darst. |
| ISBN: | 9780521197984 |
Staff View
MARC
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| 245 | 1 | 0 | |a Probability on graphs |b random processes on graphs and lattices |c Geoffrey Grimmett |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2010 | |
| 300 | |a XI, 247 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804143199079366656 |
|---|---|
| adam_text | Contents
Preface
ix
Random walks on graphs
1
1.1
Random walks and reversible Markov chains
1
1.2
Electrical networks
3
1.3
Flows and energy
8
1.4
Recurrence and resistance
11
1.5
Pólya s
theorem
14
1.6
Graph theory
16
1.7
Exercises
18
Uniform spanning tree
21
2.1
Definition
21
2.2
Wilson s algorithm
23
2.3
Weak limits on lattices
28
2.4
Uniform forest
31
2.5 Schramm-Löwner
evolutions
32
2.6
Exercises
37
Percolation and self-avoiding walk
39
3.1
Percolation and phase transition
39
3.2
Self-avoiding walks
42
3.3
Coupled percolation
45
3.4
Oriented percolation
45
3.5
Exercises
48
Association and influence
50
4.1
Holley inequality
50
4.2
FKG inequality
53
4.3
BK inequality
54
4.4
Hoeffding inequality
56
Contents
4.5
Influence for product measures
58
4.6
Proofs of influence theorems
63
4.7
Russo s formula and sharp thresholds
75
4.8
Exercises
78
Further percolation
81
5.1
Subcriticai
phase
81
5.2
Supercritical phase
86
5.3
Uniqueness of the infinite cluster
92
5.4
Phase transition
95
5.5
Open paths in
annuii
99
5.6
The critical probability in two dimensions
103
5.7
Cardy s formula
110
5.8
The critical probability via the sharp-threshold theorem
121
5.9
Exercises
125
Contact process
127
6.1
Stochastic epidemics
127
6.2
Coupling and duality
128
6.3
Invariant measures and percolation
131
6.4
The critical value
133
6.5
The contact model on a tree
135
6.6
Space-time percolation
138
6.7
Exercises
141
Gibbs states
142
7.1
Dependency graphs
142
7.2
Markov fields and Gibbs states
144
7.3
Ising and Potts models
148
7.4
Exercises
150
Random-cluster model
152
8.1
The random-cluster and Ising/Potts models
152
8.2
Basic properties
155
8.3
Infinite-volume limits and phase transition
156
8.4
Open problems
160
8.5
In two dimensions
163
8.6
Random even graphs
168
8.7
Exercises
171
Contents
vii
9 Quantum Ising
model
175
9.1
The model
175
9.2
Continuum random-cluster model
176
9.3
Quantum Ising via random-cluster
179
9.4
Long-range order
184
9.5
Entanglement in one dimension
185
9.6
Exercises
189
10
Interacting particle systems
190
10.1
Introductory remarks
190
10.2
Contact model
192
10.3
Voter model
193
10.4
Exclusion model
196
10.5
Stochastic Ising model
200
10.6
Exercises
203
11
Random graphs
205
11.1
Erdős-Rényi
graphs
205
11.2
Giant component
206
11.3
Independence and colouring
211
11.4
Exercises
217
12
Lorentz
gas
219
12.1
Lorentz
model
219
12.2
The square
Lorentz
gas
220
12.3
In the plane
223
12.4
Exercises
224
References
226
Index
243
|
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| id | DE-604.BV036598569 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:43:52Z |
| institution | BVB |
| isbn | 9780521197984 |
| language | English |
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| physical | XI, 247 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series2 | Textbooks / Institute of Mathematical Statistics |
| spelling | Grimmett, Geoffrey 1950- Verfasser (DE-588)120872919 aut Probability on graphs random processes on graphs and lattices Geoffrey Grimmett 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2010 XI, 247 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Textbooks / Institute of Mathematical Statistics 1 Hier auch später erschienene, unveränderte Nachdrucke Zufallsgraph (DE-588)4277661-2 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Zufallsgraph (DE-588)4277661-2 s DE-604 Institute of Mathematical Statistics Textbooks 1 (DE-604)BV036598560 1 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020519127&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Grimmett, Geoffrey 1950- Probability on graphs random processes on graphs and lattices Zufallsgraph (DE-588)4277661-2 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4277661-2 (DE-588)4057630-9 |
| title | Probability on graphs random processes on graphs and lattices |
| title_auth | Probability on graphs random processes on graphs and lattices |
| title_exact_search | Probability on graphs random processes on graphs and lattices |
| title_full | Probability on graphs random processes on graphs and lattices Geoffrey Grimmett |
| title_fullStr | Probability on graphs random processes on graphs and lattices Geoffrey Grimmett |
| title_full_unstemmed | Probability on graphs random processes on graphs and lattices Geoffrey Grimmett |
| title_short | Probability on graphs |
| title_sort | probability on graphs random processes on graphs and lattices |
| title_sub | random processes on graphs and lattices |
| topic | Zufallsgraph (DE-588)4277661-2 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Zufallsgraph Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020519127&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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