Products of Random Matrices with Applications to Schrödinger Operators / edited by Philippe Bougerol, Jean Lacroix
(Progress in Probability and Statistics ; 8)
| データ種別 | 電子ブック |
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| 出版者 | Boston, MA : Birkhäuser Boston |
| 出版年 | 1985 |
| 本文言語 | 英語 |
| 大きさ | XI, 284 p. 1 illus : online resource |
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| 内容注記 | A: “Limit Theorems for Products of Random Matrices” I — The Upper Lyapunov Exponent II — Matrices of Order Two III — Contraction Properties IV — Comparison of Lyapunov Exponents and Boundaries V — Central Limit Theorems and Related Results VI — Properties of the Invariant Measure and Applications B: “Random Schrödinger Operators” I — The Deterministic Schrodinger Operator II — Ergodic Schrödinger Operators III — The Pure Point Spectrum IV — Schrödinger Operators in a Strip |
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| 一般注記 | 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 196 200 5. The pure point spectrum. A criterion 6. Singularity of the spectrum 202 CHAPTER II ERGODIC SCHRÖDINGER OPERATORS 205 1. Definition and examples 205 2. General spectral properties 206 3. The Lyapunov exponent in the general ergodie case 209 4. The Lyapunov exponent in the independent eas e 211 5. Absence of absolutely continuous spectrum 221 224 6. Distribution of states. Thouless formula 232 7. The pure point spectrum. Kotani's criterion 8. Asymptotic properties of the conductance in 234 the disordered wire CHAPTER III THE PURE POINT SPECTRUM 237 238 1. The pure point spectrum. First proof 240 2. The Laplace transform on SI(2,JR) 247 3. The pure point spectrum. Second proof 250 4. The density of states CHAPTER IV SCHRÖDINGER OPERATORS IN A STRIP 2';3 1. The deterministic Schrödinger operator in 253 a strip 259 2. Ergodie Schrödinger operators in a strip 3. Lyapunov exponents in the independent case. 262 The pure point spectrum (first proof) 267 4. The Laplace transform on Sp(~,JR) 272 5. The pure point spectrum, second proof vii APPENDIX 275 BIBLIOGRAPHY 277 viii PREFACE This book presents two elosely related series of leetures. Part A, due to P |
| 著者標目 | Bougerol, Philippe editor Lacroix, Jean editor SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Matrix theory LCSH:Algebra LCSH:Partial differential equations LCSH:Probabilities FREE:Mathematics FREE:Probability Theory and Stochastic Processes FREE:Linear and Multilinear Algebras, Matrix Theory FREE:Partial Differential Equations |
| 分 類 | DC23:519.2 |
| 巻冊次 | ISBN:9781468491722 
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| ISBN | 9781468491722 |
| URL | http://dx.doi.org/10.1007/978-1-4684-9172-2 |
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