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math.PR2020
Topology and local geometry of the Eden model
Fedor Manin, Erika Roldan, Benjamin Schweinhart
The Eden cell growth model is a simple discrete stochastic process which produces a "blob" in : start with one cube in the regular grid, and at each time step add a n…
math.PR2018
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…