18 citations · 30 across the 8 of their papers we have counts for
4 papers · 1 filter
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 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…