Products of Random Matrices with Applications to Schrödinger Operators (Progress in Probability #8) (Paperback)

Products of Random Matrices with Applications to Schrödinger Operators (Progress in Probability #8) By P. Bougerol, LaCroix Cover Image

Products of Random Matrices with Applications to Schrödinger Operators (Progress in Probability #8) (Paperback)

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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 SCHR DINGER 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 SCHR DINGER OPERATORS IN A STRIP 2';3 1. The deterministic Schr dinger operator in 253 a strip 259 2. Ergodie Schr dinger 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.
Product Details ISBN: 9781468491746
ISBN-10: 1468491741
Publisher: Birkhauser
Publication Date: June 13th, 2012
Pages: 284
Language: English
Series: Progress in Probability