Random operators -- Existence of the integrated density of states -- Wegner estimate -- Wegner's original idea. Rigorous implementation -- Lipschitz continuity of the IDS -- A. Properties of the spectral shift function
Summary
The theory of random Schr??dinger operators is devoted to the mathematical analysis of quantum mechanical Hamiltonians modeling disordered solids. Apart from its importance in physics, it is a multifaceted subject in its own right, drawing on ideas and methods from various mathematical disciplines like functional analysis, selfadjoint operators, PDE, stochastic processes and multiscale methods. The present text describes in detail a quantity encoding spectral features of random operators: the integrated density of states or spectral distribution function. Various approaches to the construction
Bibliography
Includes bibliographical references (pages 113-138) and index
