Random graph dynamics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge ; New York ; Melbourne ; Madrid ; Cape Town
Cambridge University Press
2010
|
| Edition: | First paperback edition |
| Series: | Cambridge series in statistical and probabilistic mathematics
20 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | ix, 212 Seiten Illustrationen |
| ISBN: | 0521150167 9780521150163 0521866561 9780521866569 |
Staff View
MARC
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| 100 | 1 | |a Durrett, Richard |d 1951- |0 (DE-588)121396789 |4 aut | |
| 245 | 1 | 0 | |a Random graph dynamics |c Rick Durrett, Duke University |
| 250 | |a First paperback edition | ||
| 264 | 1 | |a Cambridge ; New York ; Melbourne ; Madrid ; Cape Town |b Cambridge University Press |c 2010 | |
| 300 | |a ix, 212 Seiten |b Illustrationen | ||
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| 338 | |b nc |2 rdacarrier | ||
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Record in the Search Index
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| adam_text | Contents
Preface page vii
1.
Overview I
1.1
Introduction to the Introduction
1
1.2
Erdős, Rényi,
MoUoy, and Reed
3
1.3
Six Degrees, Small Worlds
7
1.4
Power Laws, Preferential Attachment
11
1.5
Epidemics and Percolation
15
1.6
Potts Models and the Contact Process
18
1.7
Random Walks and Voter Models
20
1.8
CHKNS Model
21
2.
Erdös-Rényi
Random Graphs
27
2.1
Branching Processes
27
2.2
Cluster Growth as an Epidemic
34
2.3
Cluster Growth as a Random Walk
37
2.4
Diameter of the Giant Component
43
2.5
CLT for the Giant Component
46
2.6
Combinatorial Approach
50
2.7
Critical Regime
56
2.8
Threshold for Connectivity
62
3.
Fixed Degree Distributions
70
3.1
Definitions and Heuristics
70
3.2
Proof of Phase Transition
75
3.3
Subcriticai
Estimates
82
3.4
Distances: Finite Variance
84
3.5
Epidemics
85
4.
Power Laws
90
4.1
Barabási-
Albert Model
90
4.2
Related Models
93
4.3
Martingales and Urns
99
4.4
Scale-Free Trees
105
4.5
Distances: Power Laws
2 <
β
< 3 110
Contents
4.6 Diameter:
Barabási-Albert Model
116
4.7
Percolation, Resilience
121
4.8
SIS Epidemie
125
5.
Small Worlds
132
5.1
Watts and Strogatz Model
132
5.2
Path Lengths
134
140
144
148
153
153
156
159
164
169
171
175
177
181
187
187
190
193
197
200
203
211
5.3
Epidemics
5.4
Ising and Potts Models
5.5
Contact Process
6.
Random Walks
6.1
Spectral Gap
6.2
Conductance
6.3
Fixed Degree Distribution
6.4
Preferential Attachment Graph
6.5
Connected
Erdös-Rényi
Graphs
6.6
Small Worlds
6.7
Only Degrees
2
and
3
6.8
Hitting Times
6.9
Voter Models
7.
CHKNS Model
7.1
Heuristic Arguments
7.2
Proof of the Phase Transition
7.3
Subcriticai
Estimates
7.4
Kosterlitz-Thouless Transition
7.5
Results at the Critical Value
References
Index
|
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| id | DE-604.BV037291905 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:55:25Z |
| institution | BVB |
| isbn | 0521150167 9780521150163 0521866561 9780521866569 |
| language | English |
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| physical | ix, 212 Seiten Illustrationen |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Cambridge University Press |
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| series | Cambridge series in statistical and probabilistic mathematics |
| series2 | Cambridge series in statistical and probabilistic mathematics |
| spelling | Durrett, Richard 1951- (DE-588)121396789 aut Random graph dynamics Rick Durrett, Duke University First paperback edition Cambridge ; New York ; Melbourne ; Madrid ; Cape Town Cambridge University Press 2010 ix, 212 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Cambridge series in statistical and probabilistic mathematics 20 Hier auch später erschienene, unveränderte Nachdrucke Zufallsgraph (DE-588)4277661-2 gnd rswk-swf Zufallsgraph (DE-588)4277661-2 s DE-604 Cambridge series in statistical and probabilistic mathematics 20 (DE-604)BV011442366 20 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021204465&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Durrett, Richard 1951- Random graph dynamics Cambridge series in statistical and probabilistic mathematics Zufallsgraph (DE-588)4277661-2 gnd |
| subject_GND | (DE-588)4277661-2 |
| title | Random graph dynamics |
| title_auth | Random graph dynamics |
| title_exact_search | Random graph dynamics |
| title_full | Random graph dynamics Rick Durrett, Duke University |
| title_fullStr | Random graph dynamics Rick Durrett, Duke University |
| title_full_unstemmed | Random graph dynamics Rick Durrett, Duke University |
| title_short | Random graph dynamics |
| title_sort | random graph dynamics |
| topic | Zufallsgraph (DE-588)4277661-2 gnd |
| topic_facet | Zufallsgraph |
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