Poisson and Gaussian fluctuations for the $\mathbf{f}$-vector of high-dimensional random simplicial complexes

Jens Grygierek

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arXiv · 1911.01301

Poisson and Gaussian fluctuations for the $\mathbf{f}$-vector of high-dimensional random simplicial complexes

Jens Grygierek

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Abstract

We investigate the high-dimensional asymptotic distributional behavior of the $\mathbf{f}$-vector of a random Vietoris-Rips complex, that is generated over a stationary Poisson point process in $[-\frac{1}{2}, \frac{1}{2}]^d$ as the space dimension and the intensity tend to infinity while the radius parameter tends to zero simultaneously.

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BibTeX RIS

Jens Grygierek. 2019-11-04. Poisson and Gaussian fluctuations for the $\mathbf{f}$-vector of high-dimensional random simplicial complexes. https://arxiv.org/abs/1911.01301

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