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

zbMath1453.60014arXiv1911.01301MaRDI QIDQ5126320

Jens Grygierek

Publication date: 16 October 2020

Full work available at URL: https://arxiv.org/abs/1911.01301

zbMATH Keywords

phase transitionstochastic geometrycentral limit theoremPoisson point processPoisson limit theoremsecond-order Poincaré inequalityhigh dimensional random Vietoris-Rips complex

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Simplicial sets and complexes in algebraic topology (55U10)

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Random connection models in the thermodynamic regime: central limit theorems for add-one cost stabilizing functionals ⋮ Limit theory of sparse random geometric graphs in high dimensions

Cites Work

• Unnamed Item
• Stochastic analysis for Poisson point processes. Malliavin calculus, Wiener-Itô chaos expansions and stochastic geometry
• Normal approximation on Poisson spaces: Mehler's formula, second order Poincaré inequalities and stabilization
• Topology of random geometric complexes: a survey
• Combinatorics and commutative algebra.
• Gaussian fluctuations for edge counts in high-dimensional random geometric graphs
• Central limit theorems for \(U\)-statistics of Poisson point processes
• Random Geometric Graphs
• Lectures on the Poisson Process

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