PDE-MP-HA seminar, 7st March 2008, 1:50pm, Bloc627

Speaker: Daniel Lenz, TU Chemnitz, Germany
Title: Uniform existence of the integrated density of states for discrete
models

Abstract:

The integrated density of states of a Schroedinger operator is the limit of 
normalized eigenvalue counting functions. Usually, this limit exists in the sense 
of vague convergence of measures.  For rather general discrete models we show 
that the limit actually exists in the sense of uniform convergence of the 
corresponding distribution functions.  This is related to the eigenspace of a 
fixed energy being spanned by eigenfunctions with compact support. Examples 
include operators on quasi-transitive graphs, percolation models and 
quasicrystals.

The talk is based on joint works with Ivan Veselic and Peter Mueller.