27 citations · 166 across the 39 of their papers we have counts for
4 papers · 1 filter
Eigenvalue asymptotics for Schrödinger operators on sparse graphs
Michel Bonnefont, Sylvain Golenia, Matthias Keller
We consider Schrödinger operators on sparse graphs. The geometric definition of sparseness turn out to be equivalent to a functional inequality for the Laplacian. In consequence, s…
Graphs of finite measure
Agelos Georgakopoulos, Sebastian Haeseler, Matthias Keller +2
We consider weighted graphs with an infinite set of vertices. We show that boundedness of all functions of finite energy can be seen as a notion of `relative compactness' for such…
Harmonic functions of general graph Laplacians
Bobo Hua, Matthias Keller
We study harmonic functions on general weighted graphs which allow for a compatible intrinsic metric. We prove an Liouville type theorem which is a quantitative integral $L…
A Feynman-Kac-Itô Formula for magnetic Schrödinger operators on graphs
Batu Güneysu, Matthias Keller, Marcel Schmidt
In this paper we prove a Feynman-Kac-Itô formula for magnetic Schrödinger operators on arbitrary weighted graphs. To do so, we have to provide a natural and general framework both…