Random walks on infinite graphs and groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press
2000
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge tracts in mathematics
138 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 334 S. graph. Darst. |
| ISBN: | 0521552923 |
Internformat
MARC
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| 300 | |a XI, 334 S. |b graph. Darst. | ||
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| 490 | 1 | |a Cambridge tracts in mathematics |v 138 | |
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| 650 | 7 | |a Groepentheorie |2 gtt | |
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| 650 | 7 | |a Promenades aléatoires (Mathématiques) |2 ram | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-008785468 | ||
Datensatz im Suchindex
| _version_ | 1804127593613492224 |
|---|---|
| adam_text | CONTENTS
Preface viii
Chapter I. The type problem 1
1. Basic facts 1
A. Polya’s walk 1
B. Irreducible Markov chains 2
C. Random walks on graphs 7
D. Trees 9
E. Random walks on finitely generated groups 10
F. Locally finite graphs and topological groups 12
2. Recurrence and transience of infinite networks 14
A. Reversible Markov chains 14
B. Flows, capacity, and Nash-Williams’ criterion 18
C. Comparison with non-reversible Markov chains 23
3. Applications to random walks 25
A. Comparison theorems for random walks on graphs 25
B. Growth and the classification of recurrent groups 30
C. Random walks on quasi-transitive graphs 36
4. Isoperimetric inequalities 39
A. Isoperimetric and Sobolev inequalities 39
B. Cartesian products 43
C. Isoperimetric inequalities and growth 45
5. Transient subtrees, and the classification of the recurrent
quasi-transitive graphs 49
A. Transient subtrees 49
B. Transient subtrees in quasi-transitive graphs 54
6. More on recurrence 56
A. Generalized lattices 56
B. More on trees 62
C. Extremal length and plane tilings 67
D. Circle packings and random walks 71
Notes and remarks v 77
Chapter II. The spectral radius 81
7. Superharmonic functions and p-recurrence 81
A. The spectral radius and superharmonic functions 81
B. p-Recurrence 82
8. The spectral radius, the rate of escape, and generalized
lattices 84
v
vi
Contents
A. The rate of escape 84
B. Application to generalized lattices 88
9. Computing the Green function 93
A. Singularities of the Green function 93
B. A functional equation 98
C. Free products 101
10. The spectral radius and strong isoperimetric
inequalities 110
A. The spectral radius of reversible Markov chains 110
B. Application to random walks on graphs 112
C. Examples: trees, strongly ramified graphs, and
tilings 114
11. A lower bound for simple random walks 118
12. The spectral radius and amenability 123
A. Amenable groups 123
B. Automorphism groups and the spectral radius 125
C. Some explicit computations 129
Notes and remarks 136
Chapter III. The asymptotic behaviour of transition
probabilities 139
13. The local central limit theorem on the grid 139
14. Growth, isoperimetric inequalities, and the asymptotic
type of random walk 145
A. Upper bounds and Nash inequalities 146
B. Gaussian upper bounds 152
C. Lower bounds 157
15. The asymptotic type of random walks on amenable
groups 160
A. Comparison and stability of asymptotic type on
groups 160
B. Polycyclic groups 164
C. The solvable Baumslag-Solitar groups 168
D. Random walks on lamplighter groups 169
16. Simple random walks on the Sierpinski graphs 171
A. Stopping times and an equation for the Green
function 172
B. Singularity analysis 176
17. Local limit theorems on free products 181
A. The typical case: ra~3/2 183
B. Instability of the exponent 189
18. Intermezzo: Cartesian products 195
Contents vii
19. Free groups and homogeneous trees 199
A. Space-time asymptotics for aperiodic simple random
walks on Tm 199
B. Finite range random walks on free groups 205
C. Radial random walks on the homogeneous tree 213
Notes and remarks 216
Chapter IV. An introduction to topological
boundary theory 220
20. A probabilistic approach to the Dirichlet problem, and
a class of compactifications 220
A. The Dirichlet problem and convergence to the
boundary 220
B. Compactifications with “hyperbolic” properties 224
21. Ends of graphs and the Dirichlet problem 230
A. The transitive case 232
B. Geometric adaptedness conditions 239
22. Hyperbolic graphs and groups 242
23. The Dirichlet problem for circle packing graphs 252
24. The construction of the Martin boundary 256
25. Generalized lattices, Abelian and nilpotent groups, and
graphs with polynomial growth 262
A. Exponentials and extended exponentials 262
B. The Martin compactification of random walks on
the grid 268
26. Trees, ends, and free products 275
A. Thin ends and trees 277
B. Free products 283
27. The Martin boundary of hyperbolic graphs 288
28. Cartesian products 297
A. Minimal harmonic functions on Cartesian s
products 297
B. The Martin compactification of T x Z 301
Notes and remarks 309
Acknowledgments 315
Bibliography 316
Index 331
|
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| dewey-full | 519.2/82 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/82 |
| dewey-search | 519.2/82 |
| dewey-sort | 3519.2 282 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV012907184 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:35:49Z |
| institution | BVB |
| isbn | 0521552923 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008785468 |
| oclc_num | 41380458 |
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| physical | XI, 334 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Woess, Wolfgang 1954- Verfasser (DE-588)124183077 aut Random walks on infinite graphs and groups Wolfgang Woess 1. publ. Cambridge Cambridge Univ. Press 2000 XI, 334 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 138 Grafentheorie gtt Graphes, Théorie des ram Groepentheorie gtt Groupes infinis ram Promenades aléatoires (Mathématiques) ram Random walks (statistiek) gtt Graph theory Infinite groups Random walks (Mathematics) Unendliche Gruppe (DE-588)4375539-2 gnd rswk-swf Irrfahrt (DE-588)4561504-4 gnd rswk-swf Unendlicher Graph (DE-588)4390888-3 gnd rswk-swf Unendlicher Graph (DE-588)4390888-3 s Unendliche Gruppe (DE-588)4375539-2 s Irrfahrt (DE-588)4561504-4 s DE-604 Cambridge tracts in mathematics 138 (DE-604)BV000000001 138 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008785468&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Woess, Wolfgang 1954- Random walks on infinite graphs and groups Cambridge tracts in mathematics Grafentheorie gtt Graphes, Théorie des ram Groepentheorie gtt Groupes infinis ram Promenades aléatoires (Mathématiques) ram Random walks (statistiek) gtt Graph theory Infinite groups Random walks (Mathematics) Unendliche Gruppe (DE-588)4375539-2 gnd Irrfahrt (DE-588)4561504-4 gnd Unendlicher Graph (DE-588)4390888-3 gnd |
| subject_GND | (DE-588)4375539-2 (DE-588)4561504-4 (DE-588)4390888-3 |
| title | Random walks on infinite graphs and groups |
| title_auth | Random walks on infinite graphs and groups |
| title_exact_search | Random walks on infinite graphs and groups |
| title_full | Random walks on infinite graphs and groups Wolfgang Woess |
| title_fullStr | Random walks on infinite graphs and groups Wolfgang Woess |
| title_full_unstemmed | Random walks on infinite graphs and groups Wolfgang Woess |
| title_short | Random walks on infinite graphs and groups |
| title_sort | random walks on infinite graphs and groups |
| topic | Grafentheorie gtt Graphes, Théorie des ram Groepentheorie gtt Groupes infinis ram Promenades aléatoires (Mathématiques) ram Random walks (statistiek) gtt Graph theory Infinite groups Random walks (Mathematics) Unendliche Gruppe (DE-588)4375539-2 gnd Irrfahrt (DE-588)4561504-4 gnd Unendlicher Graph (DE-588)4390888-3 gnd |
| topic_facet | Grafentheorie Graphes, Théorie des Groepentheorie Groupes infinis Promenades aléatoires (Mathématiques) Random walks (statistiek) Graph theory Infinite groups Random walks (Mathematics) Unendliche Gruppe Irrfahrt Unendlicher Graph |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008785468&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000001 |
| work_keys_str_mv | AT woesswolfgang randomwalksoninfinitegraphsandgroups |