Conformally invariant processes in the plane:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2005]
|
| Series: | Mathematical surveys and monographs
volume 114 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | xi, 242 Seiten Illustrationen |
| ISBN: | 0821836773 9780821846247 |
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MARC
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| 100 | 1 | |a Lawler, Gregory F. |d 1955- |e Verfasser |0 (DE-588)123908671 |4 aut | |
| 245 | 1 | 0 | |a Conformally invariant processes in the plane |c Gregory F. Lawler |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2005] | |
| 264 | 4 | |c © 2005 | |
| 300 | |a xi, 242 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical surveys and monographs |v volume 114 | |
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| 650 | 4 | |a Applications conformes | |
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| 650 | 7 | |a Potentiel, Théorie du |2 ram | |
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Record in the Search Index
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| adam_text | Contents
Preface ix
Some discrete processes 1
0.1. Simple random walk 1
0.2. Loop erased random walk 3
0.3. Self avoiding walk 5
0.4. Infinitely growing self avoiding walk 7
0.5. Percolation exploration process 7
Chapter 1. Stochastic calculus 11
1.1. Definition 11
1.2. Integration with respect to Brownian motion 12
1.3. Ito s formula 17
1.4. Several Brownian motions 18
1.5. Integration with respect to semimartingales 19
1.6. Ito s formula for semimartingales 20
1.7. Time changes of martingales 22
1.8. Examples 22
1.9. Girsanov s transformation 23
1.10. Bessel processes 25
1.11. Diffusions on an interval 30
1.12. A Feynman Kac formula 39
1.13. Modulus of continuity 39
Chapter 2. Complex Brownian motion 43
2.1. Review of complex analysis 43
2.2. Conformal invariance of Brownian motion 45
2.3. Harmonic functions 46
2.4. Green s function 52
Chapter 3. Conformal mappings 57
3.1. Simply connected domains 57
3.2. Univalent functions 60
3.3. Capacity 66
3.4. Half plane capacity 69
3.5. Transformations on D 76
3.6. Caratheodory convergence 78
3.7. Extremal distance 80
3.8. Beurling estimate and applications 84
3.9. Conformal animli 88
V
vi CONTENTS
Chapter 4. Loewner differential equation 91
4.1. Chordal Loewner equation 91
4.2. Radial Loewner equation 97
4.3. Whole plane Loewner equation 100
4.4. Chains generated by curves 104
4.5. Distance to the curve 108
4.6. Perturbation by conformal maps 109
4.7. Convergence of Loewner chains 114
Chapter 5. Brownian measures on paths 119
5.1. Measures on spaces of curves 119
5.2. Brownian measures on /C 123
5.3. H excursions 130
5.4. One dimensional excursion measure 135
5.5. Boundary bubbles 137
5.6. Loop measure 141
5.7. Brownian loop soup 144
Chapter 6. Schramm Loewner evolution 147
6.1. Chordal SLE 147
6.2. Phases 150
6.3. The locality property for k = 6 152
6.4. The restriction property for k = 8/3 153
6.5. Radial SLE 156
6.6. Whole plane SLEK 162
6.7. Cardy s formula 163
6.8. SLEq in an equilateral triangle 167
6.9. Derivative estimates 169
6.10. Crossing exponent for SLEq 171
6.11. Derivative estimates, radial case 174
Chapter 7. More results about SLE 177
7.1. Introduction 177
7.2. The existence of the path 181
7.3. Holder continuity 182
7.4. Dimension of the path 183
Chapter 8. Brownian intersection exponent 187
8.1. Dimension of exceptional sets 187
8.2. Subadditivity 190
8.3. Half plane or rectangle exponent 191
8.4. Whole plane or annulus exponent 200
Chapter 9. Restriction measures 205
9.1. Unbounded hulls in H 205
9.2. Right restriction measures 209
9.3. The boundary of restriction hulls 211
9.4. Constructing restriction measures 213
Appendix A. Hausdorff dimension 217
CONTENTS vii
A.I. Definition 217
A.2. Dimension of Brownian paths 220
A.3. Dimension of random Cantor sets in [0,1] 221
Appendix B. Hypergeometric functions 229
B.I. The case a = 2/3,/? = 1/3,7 = 4/3 230
B.2. Confluent hypergeometric functions 230
B.3. Another equation 231
Appendix C. Reflecting Brownian motion 233
Appendix. Bibliography 237
Index 240
Index of symbols 242
|
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| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T20:08:11Z |
| institution | BVB |
| isbn | 0821836773 9780821846247 |
| language | English |
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| physical | xi, 242 Seiten Illustrationen |
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| series2 | Mathematical surveys and monographs |
| spelling | Lawler, Gregory F. 1955- Verfasser (DE-588)123908671 aut Conformally invariant processes in the plane Gregory F. Lawler Providence, Rhode Island American Mathematical Society [2005] © 2005 xi, 242 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs volume 114 Hier auch später erschienene, unveränderte Nachdrucke Analyse stochastique Applications conformes Invariants conformes ram Mouvement brownien, Processus de ram Potentiel, Théorie du ram Processus de Markov Processus stochastiques ram Théorie du potentiel Brownsche Bewegung (DE-588)4128328-4 gnd rswk-swf Potenzialtheorie (DE-588)4046939-6 gnd rswk-swf Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf Konforme Abbildung (DE-588)4164968-0 gnd rswk-swf Brownsche Bewegung (DE-588)4128328-4 s Stochastische Analysis (DE-588)4132272-1 s Konforme Abbildung (DE-588)4164968-0 s Potenzialtheorie (DE-588)4046939-6 s b DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1341-5 Mathematical surveys and monographs volume 114 (DE-604)BV000018014 114 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013201617&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lawler, Gregory F. 1955- Conformally invariant processes in the plane Mathematical surveys and monographs Analyse stochastique Applications conformes Invariants conformes ram Mouvement brownien, Processus de ram Potentiel, Théorie du ram Processus de Markov Processus stochastiques ram Théorie du potentiel Brownsche Bewegung (DE-588)4128328-4 gnd Potenzialtheorie (DE-588)4046939-6 gnd Stochastische Analysis (DE-588)4132272-1 gnd Konforme Abbildung (DE-588)4164968-0 gnd |
| subject_GND | (DE-588)4128328-4 (DE-588)4046939-6 (DE-588)4132272-1 (DE-588)4164968-0 |
| title | Conformally invariant processes in the plane |
| title_auth | Conformally invariant processes in the plane |
| title_exact_search | Conformally invariant processes in the plane |
| title_full | Conformally invariant processes in the plane Gregory F. Lawler |
| title_fullStr | Conformally invariant processes in the plane Gregory F. Lawler |
| title_full_unstemmed | Conformally invariant processes in the plane Gregory F. Lawler |
| title_short | Conformally invariant processes in the plane |
| title_sort | conformally invariant processes in the plane |
| topic | Analyse stochastique Applications conformes Invariants conformes ram Mouvement brownien, Processus de ram Potentiel, Théorie du ram Processus de Markov Processus stochastiques ram Théorie du potentiel Brownsche Bewegung (DE-588)4128328-4 gnd Potenzialtheorie (DE-588)4046939-6 gnd Stochastische Analysis (DE-588)4132272-1 gnd Konforme Abbildung (DE-588)4164968-0 gnd |
| topic_facet | Analyse stochastique Applications conformes Invariants conformes Mouvement brownien, Processus de Potentiel, Théorie du Processus de Markov Processus stochastiques Théorie du potentiel Brownsche Bewegung Potenzialtheorie Stochastische Analysis Konforme Abbildung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013201617&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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