The study of disorder has generated enormous research activity in mathematics and physics. Over the past 15 years various aspects of the subject have changed a number of paradigms and have inspired the discovery of deep mathematical techniques to deal with complex problems arising from the effects of disorder. One important effect is a phenomenon called localization, which describes the very strange behavior of waves in random media---the fact that waves, instead of traveling through space as they do in ordered environments, stay in a confined region (caught by disorder). To date, there is no treatment of this subject in monograph or textbook form. This book fills that gap.
Caught by Disorder presents:
* an introduction to disorder that can be grasped by graduate students in a hands-on way
* a concise, mathematically rigorous examination of some particular models of disordered systems
* a detailed application of the localization phenomenon, worked out in two typical model classes that keep the technicalities at a reasonable level
* a thorough examination of new mathematical machinery, in particular, the method of multiscale analysis
* a number of key unsolved problems
* an appendix containing the prerequisites of operator theory, as well as other proofs
* examples, illustrations, comprehensive bibliography, author and keyword index
Mathematical background for this book requires only a knowledge of partial differential equations, functional analysis---mainly operator theory and spectral theory---and elementary probability theory. The work is an excellent text for a graduate course or seminar in mathematical physics or serves as a standard reference for specialists.

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