3 papers
math-ph2011
Absolutely continuous spectrum for random operators on trees of finite cone type
Matthias Keller, Daniel Lenz, Simone Warzel
We study the spectrum of random operators on a large class of trees. These trees have finitely many cone types and they can be constructed by a substitution rule. The random operat…
math.FA2011
Unbounded Laplacians on Graphs: Basic Spectral Properties and the Heat Equation
Matthias Keller, Daniel Lenz
We discuss Laplacians on graphs in a framework of regular Dirichlet forms. We focus on phenomena related to unboundedness of the Laplacians. This includes (failure of) essential se…
math.CO2011
Curvature, geometry and spectral properties of planar graphs
Matthias Keller
We introduce a curvature function for planar graphs to study the connection between the curvature and the geometric and spectral properties of the graph. We show that non-positive…