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Products of Random Matrices with Applications to Schrödinger Operators

Products of Random Matrices with Applications to Schrödinger Operators
Catalogue Information
Field name Details
Dewey Class 519.2
Title Products of Random Matrices with Applications to Schrödinger Operators ([EBook] /) / edited by Philippe Bougerol, Jean Lacroix.
Added Personal Name Bougerol, Philippe editor.
Lacroix, Jean editor.
Other name(s) SpringerLink (Online service)
Publication Boston, MA : : Birkhäuser Boston, , 1985.
Physical Details XI, 284 p. 1 illus. : online resource.
Series Progress in probability and statistics ; 8
ISBN 9781468491722
Summary Note 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.:
Contents note 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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