Random connection models in the thermodynamic regime: central limit theorems for add-one cost stabilizing functionals

DOI10.1214/22-EJP759zbMath1491.60040arXiv2004.06313WikidataQ113751959 ScholiaQ113751959MaRDI QIDQ2119689

Trinh Khanh Duy, Van Hao Can

Publication date: 30 March 2022

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.06313

zbMATH Keywords

central limit theoremBetti numbersrandom connection modelclique complexweak stabilization

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Random graphs (graph-theoretic aspects) (05C80) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Cites Work

• Unnamed Item
• Unnamed Item
• Connectivity of soft random geometric graphs over annuli
• Random geometric complexes in the thermodynamic regime
• Random geometric complexes
• Normal approximation on Poisson spaces: Mehler's formula, second order Poincaré inequalities and stabilization
• Subcritical regimes in the Poisson Boolean model of continuum percolation
• Topology of random clique complexes
• Domination by product measures
• Limit theorems for persistence diagrams
• A remark on the convergence of Betti numbers in the thermodynamic regime
• Strong law of large numbers for Betti numbers in the thermodynamic regime
• Gaussian limits for random measures in geometric probability
• High density asymptotics of the Poisson random connection model
• Limit theory for random sequential packing and deposition
• Central limit theorems for some graphs in computational geometry.
• Subcritical phase of \(d\)-dimensional Poisson-Boolean percolation and its vacant set
• The random connection model and functions of edge-marked Poisson processes: second order properties and normal approximation
• On central limit theorems in stochastic geometry for add-one cost stabilizing functionals
• The Random Connection Model on the Torus
• Random Geometric Graphs
• The random connection model: Connectivity, edge lengths, and degree distributions
• Continuum Percolation
• Poisson and Gaussian fluctuations for the $\mathbf{f}$-vector of high-dimensional random simplicial complexes
• Lectures on the Poisson Process
• Random Networks for Communication