On central limit theorems in stochastic geometry for add-one cost stabilizing functionals

Khanh Duy Trinh

doi:10.1214/19-ECP279

On central limit theorems in stochastic geometry for add-one cost stabilizing functionals

Khanh Duy Trinh^*

^*Corresponding author for this work

Global Center for Science and Engineering

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

We establish central limit theorems for general functionals on binomial point processes and their Poissonized version, which extends the results of Penrose–Yukich (Ann. Appl. Probab. 11(4), 1005–1041 (2001)) to the inhomogeneous case. Here functionals are required to be strongly stabilizing for add-one cost on homogeneous Poisson point processes and to satisfy some moments conditions. As an application, a central limit theorem for Betti numbers of random geometric complexes in the subcritical regime is derived.

Original language	English
Pages (from-to)	1-15
Number of pages	15
Journal	Electronic Communications in Probability
Volume	24
DOIs	https://doi.org/10.1214/19-ECP279
Publication status	Published - 2019

Keywords

Add-one cost
Betti numbers
Central limit theorem
Critical regime
De-Poissonization
Stochastic geometry
Strong stabilization

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/19-ECP279

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abstract = "We establish central limit theorems for general functionals on binomial point processes and their Poissonized version, which extends the results of Penrose–Yukich (Ann. Appl. Probab. 11(4), 1005–1041 (2001)) to the inhomogeneous case. Here functionals are required to be strongly stabilizing for add-one cost on homogeneous Poisson point processes and to satisfy some moments conditions. As an application, a central limit theorem for Betti numbers of random geometric complexes in the subcritical regime is derived.",

keywords = "Add-one cost, Betti numbers, Central limit theorem, Critical regime, De-Poissonization, Stochastic geometry, Strong stabilization",

author = "Trinh, {Khanh Duy}",

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AU - Trinh, Khanh Duy

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PY - 2019

Y1 - 2019

N2 - We establish central limit theorems for general functionals on binomial point processes and their Poissonized version, which extends the results of Penrose–Yukich (Ann. Appl. Probab. 11(4), 1005–1041 (2001)) to the inhomogeneous case. Here functionals are required to be strongly stabilizing for add-one cost on homogeneous Poisson point processes and to satisfy some moments conditions. As an application, a central limit theorem for Betti numbers of random geometric complexes in the subcritical regime is derived.

AB - We establish central limit theorems for general functionals on binomial point processes and their Poissonized version, which extends the results of Penrose–Yukich (Ann. Appl. Probab. 11(4), 1005–1041 (2001)) to the inhomogeneous case. Here functionals are required to be strongly stabilizing for add-one cost on homogeneous Poisson point processes and to satisfy some moments conditions. As an application, a central limit theorem for Betti numbers of random geometric complexes in the subcritical regime is derived.

KW - Add-one cost

KW - Betti numbers

KW - Central limit theorem

KW - Critical regime

KW - De-Poissonization

KW - Stochastic geometry

KW - Strong stabilization

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JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

ER -

On central limit theorems in stochastic geometry for add-one cost stabilizing functionals

Abstract

Keywords

ASJC Scopus subject areas

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