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Progress in Probability

Products of Random Matrices with Applications to Schrödinger Operators

Authors: Bougerol, P., Lacroix

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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 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.

Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook $84.99
price for USA in USD
  • ISBN 978-1-4684-9172-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Products of Random Matrices with Applications to Schrödinger Operators
Authors
Series Title
Progress in Probability
Series Volume
8
Copyright
1985
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston, Inc.
eBook ISBN
978-1-4684-9172-2
DOI
10.1007/978-1-4684-9172-2
Softcover ISBN
978-1-4684-9174-6
Series ISSN
1050-6977
Edition Number
1
Number of Pages
XI, 284
Number of Illustrations
1 b/w illustrations
Topics