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

Jens Grygierek

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

Probability 2019-11-05 v1

Authors: Jens Grygierek

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.

Keywords

random simplicial complex vietoris-rips complex f-vector poisson point process poisson fluctuation gaussian fluctuation high-dimensional asymptotics

Cite

@article{arxiv.1911.01301,
  title  = {Poisson and Gaussian fluctuations for the $\mathbf{f}$-vector of high-dimensional random simplicial complexes},
  author = {Jens Grygierek},
  journal= {arXiv preprint arXiv:1911.01301},
  year   = {2019}
}

Comments

33 pages

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