1 citations · 1 across the 3 of their papers we have counts for
4 papers
Quantitative concentration inequalities for the uniform approximation of the IDS
Max Kämper, Christoph Schumacher, Fabian Schwarzenberger +1
The integrated density of states (IDS) is a fundamental spectral quantity for quantum Hamiltonians modeling condensed matter systems, describing how densely energy levels are distr…
Uniform existence of the IDS on lattices and groups
Christoph Schumacher, Fabian Schwarzenberger, Ivan Veselic
We present a general framework for thermodynamic limits and its applications to a variety of models. In particular we will identify criteria such that the limits are uniform in a p…
Approximation of the integrated density of states on sofic groups
Christoph Schumacher, Fabian Schwarzenberger
In this paper we study spectral properties of self-adjoint operators on a large class of geometries given via sofic groups. We prove that the associated integrated densities of sta…
Uniform approximation of the integrated density of states for long-range percolation Hamiltonians
Fabian Schwarzenberger
In this paper we study the spectrum of long-range percolation graphs. The underlying geometry is given in terms of a finitely generated amenable group. We prove that the integrated…