Products of random matrices with applications to Schrödinger operators:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Boston ; Basel ; Stuttgart
Birkhäuser
1985
|
| Schriftenreihe: | Progress in probability and statistics
8 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000239794&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | x, 283 Seiten |
| ISBN: | 3764333243 0817633243 9781468491722 |
Internformat
MARC
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| 100 | 1 | |a Bougerol, Philippe |d 1951- |0 (DE-588)171986288 |4 aut | |
| 245 | 1 | 0 | |a Products of random matrices with applications to Schrödinger operators |c Philippe Bougerol ; Jean Lacroix |
| 264 | 1 | |a Boston ; Basel ; Stuttgart |b Birkhäuser |c 1985 | |
| 300 | |a x, 283 Seiten | ||
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| 490 | 1 | |a Progress in probability and statistics |v 8 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-000239794 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 600f 2001 A 8417 |
|---|---|
| DE-BY-TUM_katkey | 67846 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010630125 |
| _version_ | 1821939728045309952 |
| adam_text | CONTENTS
PART A : LIMIT THEOREMS FOR PRODUCTS OF RANDOM MATRICES
INTRODUCTION 1
CHAPTER I - THE UPPER LYAPUNOV EXPONENT 5
1. Notation 5
2. The upper Lyapunov exponent ...... 6
3. Cocycles .......... 8
4. The theorem of Furstenberg and Kesten ... 11
5. Exercises 13
CHAPTER II - MATRICES OF ORDER TWO 17
1. The set-up 17
2. Two basic lemmas 19
3. Contraction properties 24
4. Furstenberg s theorem 30
5. Some simple examples ....... 33
6. Exercises 36
7. Complements 38
CHAPTER III - CONTRACTION PROPERTIES 43
1 . Contracting sets 44
2. Strong irreducibility 48
3. A key property 50
4. Contracting action on P(IR ) and convergence in
direction 55
v
5. Lyapunov exponents 60
6. Comparison of the top Lyapunov exponents and
Furstenberg s theorem 64
7. Complements. The irreducible case .... 68
CHAPTER IV - COMPARISON OF LYAPUNOV EXPONENTS AND
BOUNDARIES 77
1. A criterion ensuring that Lyapunov exponents
are distinct 77
2. Some examples ......... 81
3. The case of symplectic matrices .... 87
4. u-boundaries 93
CHAPTER V - CENTRAL LIMIT THEOREMS AND RELATED RESULTS . 101
1. Introduction 101
2. Exponential convergence to the invariant
measure .......... 103
3. A lemma of perturbation theory 111
4. The Fourier-Laplace transform near 0 . . 116
5. Central limit theorem 121
6. Large deviations 129
7. Convergence to y 134
8. Convergence in distribution without
normalization ......... 135
9. Complements : linear stochastic differential
equations .......... 1*0
CHAPTER VI - PROPERTIES OF THE INVARIANT MEASURE AND
APPLICATIONS 1*5
1. Convergence in the Iwasawa decomposition . . 1*7
2. Limit theorems for the coefficients ... 155
3. Behaviour of the rows ....... 159
4. Regularity of the invariant measure ... 161
5. An example : random continued fractions . 166
SUGGESTIONS FOR FURTHER READINGS 1 73
BIBLIOGRAPHY 175
vi
PART B : RANDOM SCHRODINGER OPERATORS
INTRODUCTION 183
CHAPTER I - THE DETERMINISTIC SCHRODINGER OPERATOR . . 187
1. The difference equation. Hyperbolic structures . 187
2. Self adjointness of H. Spectral properties . . 190
3. Slowly increasing generalized eigenfunctions . 195
4. Approximations of the spectral measure ... 196
5. The pure point spectrum. A criterion . . . 200
6. Singularity of the spectrum 202
CHAPTER II - ERGODIC SCHRODINGER OPERATORS .... 205
1 . Definition and examples 205
2. General spectral properties 206
3. The Lyapunov exponent in the general ergodic
case 209
4. The Lyapunov exponent in the independent case . 211
5. Absence of absolutely continuous spectrum . . 221
6. Distribution of states. Thouless formula . . 224
7. The pure point spectrum. Kotani s criterion . 232
8. Asymptotic properties of the conductance in
the disordered wire 234
CHAPTER III - THE PURE POINT SPECTRUM 237
1 . The pure point spectrum. First proof . . . 238
2. The Laplace transform on S1(2,K) . . . . 240
3. The pure point spectrum. Second proof . . . 247
4. The density of states 250
CHAPTER IV - SCHRODINGER OPERATORS IN A STRIP ... 253
1 . The deterministic Schrb dinger operator in
a strip 253
2. Ergodic Schrb dinger operators in a strip . . 259
3. Lyapunov exponents in the independent case.
The pure point spectrum (first proof) . . . 262
4. The Laplace transform on Sp(5,,]R) .... 267
5. The pure point spectrum, second proof . . . 272
vii
APPENDIX 275
BIBLIOGRAPHY 277
viii
|
| any_adam_object | 1 |
| author | Bougerol, Philippe 1951- Lacroix, Jean |
| author_GND | (DE-588)171986288 (DE-588)1292708166 |
| author_facet | Bougerol, Philippe 1951- Lacroix, Jean |
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| author_sort | Bougerol, Philippe 1951- |
| author_variant | p b pb j l jl |
| building | Verbundindex |
| bvnumber | BV000386489 |
| classification_rvk | SK 620 SK 800 SK 820 SK 835 |
| classification_tum | MAT 474f MAT 600f |
| ctrlnum | (OCoLC)440653721 (DE-599)BVBBV000386489 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000386489 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T07:20:10Z |
| institution | BVB |
| isbn | 3764333243 0817633243 9781468491722 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000239794 |
| oclc_num | 440653721 |
| open_access_boolean | |
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| physical | x, 283 Seiten |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in probability and statistics |
| series2 | Progress in probability and statistics |
| spellingShingle | Bougerol, Philippe 1951- Lacroix, Jean Products of random matrices with applications to Schrödinger operators Progress in probability and statistics Stochastische Matrix (DE-588)4057624-3 gnd Hamilton-Operator (DE-588)4072278-8 gnd |
| subject_GND | (DE-588)4057624-3 (DE-588)4072278-8 |
| title | Products of random matrices with applications to Schrödinger operators |
| title_auth | Products of random matrices with applications to Schrödinger operators |
| title_exact_search | Products of random matrices with applications to Schrödinger operators |
| title_full | Products of random matrices with applications to Schrödinger operators Philippe Bougerol ; Jean Lacroix |
| title_fullStr | Products of random matrices with applications to Schrödinger operators Philippe Bougerol ; Jean Lacroix |
| title_full_unstemmed | Products of random matrices with applications to Schrödinger operators Philippe Bougerol ; Jean Lacroix |
| title_short | Products of random matrices with applications to Schrödinger operators |
| title_sort | products of random matrices with applications to schrodinger operators |
| topic | Stochastische Matrix (DE-588)4057624-3 gnd Hamilton-Operator (DE-588)4072278-8 gnd |
| topic_facet | Stochastische Matrix Hamilton-Operator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000239794&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000010596 |
| work_keys_str_mv | AT bougerolphilippe productsofrandommatriceswithapplicationstoschrodingeroperators AT lacroixjean productsofrandommatriceswithapplicationstoschrodingeroperators |
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 600f 2001 A 8417 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |