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math.FA2026
The complex property of the boundary operator on simplicial complexes
Philipp Bartmann, Matthias Keller
We study the complex property of the boundary operator on a weighted, infinite, and possibly non-locally finite simplicial complex. We give a char…
math.FA2026
Graphs at infinity: Liouville theorems, Recurrence and Characterization of Dirichlet forms
Matthias Keller, Daniel Lenz, Marcel Schmidt
We survey recent results on graphs and their Laplacians related to the behavior of the graph at large. In particular, we focus on Liouville theorems, recurrence and characterizatio…