The theory of random Schrodinger 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 of the integrated density of states and the proof of
its regularity properties are presented.
The setting is general enough to apply to random operators on
Riemannian manifolds with a discrete group action. References to
and a discussion of other properties of the IDS are included, as
are a variety of models beyond those treated in detail here.
General
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