Brownian Brownian motion-I:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Math. Soc.
2009
|
| Series: | Memoirs of the American Mathematical Society
927 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "Volume 198, number 927 (fourth of 6 numbers )." Literaturverz. S. 187 - 191 |
| Physical Description: | VII, 193 S. graph. Darst. |
| ISBN: | 9780821842829 |
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Record in the Search Index
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| adam_text | Titel: Brownian Brownian motion I
Autor: Chernov, Nikolai
Jahr: 2009
Contents
Chapter 1. Introduction 1
1.1. The model 1
1.2. The container 2
1.3. Billiard approximations 3
Chapter 2. Statement of results 7
2.1. Heavy disk in equilibrium (linear motion) 7
2.2. Heavy disk at rest (slow acceleration) 9
2.3. Heavy disk of small size 11
2.4. Comparison to previous works 12
Chapter 3. Plan of the proofs 15
3.1. General strategy 15
3.2. Precise definitions 17
3.3. Key technical results 20
Chapter 4. Standard pairs and equidistribution 25
4.1. Unstable vectors 25
4.2. Unstable curves 29
4.3. Homogeneous unstable curves 33
4.4. Standard pairs 36
4.5. Perturbative analysis 42
4.6. Equidistribution properties 47
Chapter 5. Regularity of the diffusion matrix 57
5.1. Transport coefficients 57
5.2. Reduction to a finite series 62
5.3. Integral estimates: general scheme 64
5.4. Integration by parts 69
5.5. Cancellation of large boundary terms 77
5.6. Estimation of small boundary terms 81
5.7. Two-sided integral sums 84
5.8. Bounding off-diagonal terms 88
5.9. Holder approximation 90
Chapter 6. Moment estimates 93
V
vi CONTENTS
6.1. General plan 93
6.2. Structure of the proofs 98
6.3. Short term moment estimates for V 100
6.4. Moment estimates-a priori bounds 103
6.5. Tightness 110
6.6. Second moment 113
6.7. Martingale property 115
6.8. Transition to continuous time 117
6.9. Uniqueness for stochastic differential equations 118
Chapter 7. Fast slow particle 123
Chapter 8. Small large particle 129
Chapter 9. Open problems 133
9.1. Collisions of the massive disk with the wall 133
9.2. Longer time scales 133
9.3. Stadia and the piston problem 133
9.4. Finitely many particles 134
9.5. Growing number of particles 135
9.6. Particles of positive size 136
Appendix A. Statistical properties of dispersing billiards 139
A.I. Decay of correlations: overview 139
A.2. Decay of correlations: extensions 149
A.3. Large deviations 153
A.4. Moderate deviations 154
A.5. Nonsingularity of diffusion matrix 158
A.6. Asymptotics of diffusion matrix 159
Appendix B. Growth and distortion in dispersing billiards 167
B.I. Regularity of H-curves 167
B.2. Invariant Section Theorem 171
B.3. The function space 91 174
Appendix C. Distortion bounds for two particle system 177
Bibliography 187
Index 193
|
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| author_sort | Černov, Nikolaj 1956-2014 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV035456740 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:35:41Z |
| institution | BVB |
| isbn | 9780821842829 |
| language | English |
| lccn | 2008047662 |
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| physical | VII, 193 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Černov, Nikolaj 1956-2014 Verfasser (DE-588)141030992 aut Brownian Brownian motion-I N. Chernov ; D. Dolgopyat Providence, R.I. American Math. Soc. 2009 VII, 193 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 927 "Volume 198, number 927 (fourth of 6 numbers )." Literaturverz. S. 187 - 191 Diffusion processes Brownian movements Limit theorems (Probability theory) Brownsche Bewegung (DE-588)4128328-4 gnd rswk-swf Diffusionsprozess (DE-588)4274463-5 gnd rswk-swf Diffusionsprozess (DE-588)4274463-5 s Brownsche Bewegung (DE-588)4128328-4 s DE-604 Dolgopyat, Dmitry 1972- Verfasser (DE-588)137737734 aut Memoirs of the American Mathematical Society 927 (DE-604)BV008000141 927 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017376668&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Černov, Nikolaj 1956-2014 Dolgopyat, Dmitry 1972- Brownian Brownian motion-I Memoirs of the American Mathematical Society Diffusion processes Brownian movements Limit theorems (Probability theory) Brownsche Bewegung (DE-588)4128328-4 gnd Diffusionsprozess (DE-588)4274463-5 gnd |
| subject_GND | (DE-588)4128328-4 (DE-588)4274463-5 |
| title | Brownian Brownian motion-I |
| title_auth | Brownian Brownian motion-I |
| title_exact_search | Brownian Brownian motion-I |
| title_full | Brownian Brownian motion-I N. Chernov ; D. Dolgopyat |
| title_fullStr | Brownian Brownian motion-I N. Chernov ; D. Dolgopyat |
| title_full_unstemmed | Brownian Brownian motion-I N. Chernov ; D. Dolgopyat |
| title_short | Brownian Brownian motion-I |
| title_sort | brownian brownian motion i |
| topic | Diffusion processes Brownian movements Limit theorems (Probability theory) Brownsche Bewegung (DE-588)4128328-4 gnd Diffusionsprozess (DE-588)4274463-5 gnd |
| topic_facet | Diffusion processes Brownian movements Limit theorems (Probability theory) Brownsche Bewegung Diffusionsprozess |
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