75 citations · 932 across the 61 of their papers we have counts for
3 papers · 1 filter
Random walks on barycentric subdivisions and the Strichartz hexacarpet
Matthew Begue, Daniel J. Kelleher, Aaron Nelson +3
We investigate the relation between simple random walks on repeated barycentric subdivisions of a triangle and a self-similar fractal, Strichartz hexacarpet, which we introduce. We…
Derivations and Dirichlet forms on fractals
Marius Ionescu, Luke G. Rogers, Alexander Teplyaev
We study derivations and Fredholm modules on metric spaces with a local regular conservative Dirichlet form. In particular, on finitely ramified fractals, we show that there is a n…
Disconnected Julia sets and gaps in the spectrum of Laplacians on symmetric finitely ramified fractals
Katheryn Hare, Benjamin Steinhurst, Alexander Teplyaev +1
It is known that Laplacian operators on many fractals have gaps in their spectra. This fact precludes the possibility that a Weyl-type ratio can have a limit and is also a key ingr…