16 citations · 16 across the 2 of their papers we have counts for
4 papers
Invertibility of graph translation and support of Laplacian Fiedler vectors
Matthew Begué, Kasso A. Okoudjou
The graph Laplacian operator is widely studied in spectral graph theory largely due to its importance in modern data analysis. Recently, the Fourier transform and other time-freque…
Harmonic functions and the spectrum of the Laplacian on the Sierpinski carpet
Matthew Begue, Tristan Kalloniatis, Robert S. Strichartz
Kusuoka and Zhou have defined the Laplacian on the Sierpinski carpet using average values of functions on small cells and the graph structure of cell adjacency. We have implemented…
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…
Spectrum and Heat Kernel Asymptotics on General Laakso Spaces
Matthew Begue, Levi DeValve, David Miller +1
We introduce a method of constructing a general Laakso space while calculating the spectrum and multiplicities of the Laplacian operator on it. Using this information, we found the…