18 citations · 30 across the 8 of their papers we have counts for
10 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…
Glivenko-Cantelli Theory, Ornstein-Weiss quasi-tilings, and uniform Ergodic Theorems for distribution-valued fields over amenable groups
Christoph Schumacher, Fabian Schwarzenberger, Ivan Veselic
We consider random fields indexed by finite subsets of an amenable discrete group, taking values in the Banach-space of bounded right-continuous functions. The field is assumed to…
A Glivenko-Cantelli Theorem for almost additive functions
Christoph Schumacher, Fabian Schwarzenberger, Ivan Veselic
We develop a Glivenko--Cantelli theory for monotone, almost additive functions of i.\,i.\,d.\ sequences of random variables indexed by~. Under certain conditions on the rando…
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 existence of the integrated density of states for randomly weighted Hamiltonians on long-range percolation graphs
Slim Ayadi, Fabian Schwarzenberger, Ivan Veselic
In this paper we consider random Hamiltonians defined on long-range percolation graphs over $\ZZ^d$. The Hamiltonian consists of a randomly weighted Laplacian plus a random potenti…
A Banach space-valued ergodic theorem for amenable groups and applications
Felix Pogorzelski, Fabian Schwarzenberger
In this paper we study unimodular amenable groups. The first part is devoted to results on the existence of uniform families of epsilon-quasi tilings for these groups. In this cont…
Uniform existence of the integrated density of states on metric Cayley graphs
Felix Pogorzelski, Fabian Schwarzenberger, Christian Seifert
Given a finitely generated amenable group we consider ergodic random Schrödinger operators on a Cayley graph with random potentials and random boundary conditions. We show that the…
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…
A Banach space-valued ergodic theorem and the uniform approximation of the integrated density of states
Daniel Lenz, Fabian Schwarzenberger, Ivan Veselić
In this paper we consider bounded operators on infinite graphs, in particular Cayley graphs of amenable groups. The operators satisfy an equivariance condition which is formulated…