34 citations · 49 across the 20 of their papers we have counts for
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math.PR2018★ 3 cited
Fractal Dimension and the Persistent Homology of Random Geometric Complexes
Benjamin Schweinhart
We prove that the fractal dimension of a metric space equipped with an Ahlfors regular measure can be recovered from the persistent homology of random samples. Our main result is t…
math.PR2018
Weighted Persistent Homology Sums of Random Čech Complexes
Benjamin Schweinhart
We study the asymptotic behavior of random variables of the form \begin{equation*} E_α^i\left(x_1,\ldots,x_n\right)=\sum_{\left(b,d\right)\in \mathit{PH}_i\left(x_1,\ldots,x_n\righ…
math.MG2018
Persistent Homology and the Upper Box Dimension
Benjamin Schweinhart
We introduce a fractal dimension for a metric space defined in terms of the persistent homology of extremal subsets of that space. We exhibit hypotheses under which this dimension…