31 citations · 42 across the 3 of their papers we have counts for
3 papers
math.SP2007★ 3 cited
Optimal Wegner estimates for random Schroedinger operators on metric graphs
Michael J. Gruber, Mario Helm, Ivan Veselic
We consider Schroedinger operators with a random potential of alloy type on infinite metric graphs which obey certain uniformity conditions. For single site potentials of fixed sig…
math-ph2006★ 31 cited
Localization on a quantum graph with a random potential on the edges
Pavel Exner, Mario Helm, Peter Stollmann
We prove spectral and dynamical localization on a cubic-lattice quantum graph with a random potential. We use multiscale analysis and show how to obtain the necessary estimates in…
math.SP2006★ 8 cited
A linear Wegner estimate for alloy type Schroedinger operators on metric graphs
Mario Helm, Ivan Veselic'
We study spectra of alloy-type random Schrödinger operators on metric graphs. For finite edge subsets of general graphs we prove a Wegner estimate which is linear in the volume (i.…