56 citations · 143 across the 13 of their papers we have counts for
5 papers · 1 filter
Spectral dimension of trees with a unique infinite spine
Sigurdur Orn Stefansson, Stefan Zohren
Using generating functions techniques we develop a relation between the Hausdorff and spectral dimension of trees with a unique infinite spine. Furthermore, it is shown that if the…
Condensation in nongeneric trees
Thordur Jonsson, Sigurdur Orn Stefansson
We study nongeneric planar trees and prove the existence of a Gibbs measure on infinite trees obtained as a weak limit of the finite volume measures. It is shown that in the infini…
Appearance of vertices of infinite order in a model of random trees
Thordur Jonsson, Sigurdur O. Stefansson
We study an equilibrium statistical mechanical model of tree graphs which are made up of a linear subgraph (the spine) to which leaves are attached. We prove that the model has two…
Random tree growth by vertex splitting
Francois David, Mark Dukes, Thordur Jonsson +1
We study a model of growing planar tree graphs where in each time step we separate the tree into two components by splitting a vertex and then connect the two pieces by inserting a…
The spectral dimension of random brushes
Thordur Jonsson, Sigurdur Orn Stefansson
We consider a class of random graphs, called random brushes, which are constructed by adding linear graphs of random lengths to the vertices of Z^d viewed as a graph. We prove that…