Caught by Disorder: Bound States in Random Media

Introduction * 1. Getting Started * 1.1. Bound States versus Extended States * 1.2. Ergodic Operator Families * 1.3. Some Important Examples * 1.4. Our Basic Models (P + A) and (DIV) * 1.5. Localization and Lifshitz Tails: The Heuristic Picture * 2. Analysis of Anderson-type Models * 2.1. Lifshitz Tails for (P + A) * 2.2. Initial Length Scale Estimates * 2.3. Wegner Estimates * 2.4. Combes--Thomas Estimates * 2.5. Changing Cubes * 3. Multiscale Analysis * 3.1. Idea of the Proof of Localization and Historical Notes * 3.2. Multiscale Analysis * 3.3. Exponential Localization * 3.4. Dynamical Localization * 3.5. More Models * 4. Appendix * 4.1. A Short Story of Selfadjoint Operators * 4.2. Some Basics from Probability Theory * 5. Aftermath * References * Index