4 papers
The spectra of graph substitutions
Thomas Hirschler, Wolfgang Woess
Let and be finite connected graphs without loops. We assume that has two distinguished vertices and an automorphism which exchanges and~. T…
Laplace and bi-Laplace equations for directed networks and Markov chains
Thomas Hirschler, Wolfgang Woess
The networks of this -- primarily (but not exclusively) expository -- compendium are strongly connected, finite directed graphs , where each oriented edge is equipped wi…
Polyharmonic functions for finite graphs and Markov chains
Thomas Hirschler, Wolfgang Woess
On a finite graph with a chosen partition of the vertex set into interior and boundary vertices, a -polyharmonic function is a complex function on the vertex set which satis…
Comparing entropy rates on finite and infinite rooted trees
Thomas Hirschler, Wolfgang Woess
We consider stochastic processes with (or without) memory whose evolution is encoded by a finite or infinite rooted tree. The main goal is to compare the entropy rates of a given b…