Normal convergence of nonlocalised geometric functionals and shot-noise excursions

DOI10.1214/18-AAP1445zbMath1448.60057arXiv1712.01558OpenAlexW2980344430MaRDI QIDQ2286446

Raphael Lachieze-Rey

Publication date: 22 January 2020

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.01558

zbMATH Keywords

central limit theoremstabilisationBerry-Esseen boundsPoisson functionalsshot-noise fieldsrandom excursions

Mathematics Subject Classification ID

Random fields (60G60) Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05)

Related Items (6)

Percolation of the excursion sets of planar symmetric shot noise fields ⋮ Variance asymptotics and central limit theory for geometric functionals of Poisson cylinder processes ⋮ On the excursion area of perturbed Gaussian fields ⋮ Statistical inference on stationary shot noise random fields ⋮ Testing marginal symmetry of digital noise images through the perimeter of excursion sets ⋮ Quantitative two-scale stabilization on the Poisson space

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the perimeter of excursion sets of shot noise random fields
• Central limit theorems for the excursion set volumes of weakly dependent random fields
• A central limit theorem for the Euler characteristic of a Gaussian excursion set
• Normal approximation on Poisson spaces: Mehler's formula, second order Poincaré inequalities and stabilization
• Sums of functions of nearest neighbor distances, moment bounds, limit theorems and a goodness of fit test
• New Berry-Esseen bounds for functionals of binomial point processes
• Lipschitz-Killing curvatures of excursion sets for two-dimensional random fields
• Normal approximation for stabilizing functionals
• Central limit theorem for exponentially quasi-local statistics of spin models on Cayley graphs
• Central limit theorems for some graphs in computational geometry.
• Crossings of smooth shot noise processes
• Mean geometry for 2D random fields: level perimeter and level total curvature integrals
• On volume and surface area of parallel sets
• Random measurable sets and covariogram realizability problems
• Detecting Dependence Between Marks and Locations of Marked Point Processes
• Stochastic Geometry and Wireless Networks: Volume II Applications
• On Scaling Limits of Power Law Shot-Noise Fields
• Large deviation principles for Euclidean functionals and other nearly additive processes

This page was built for publication: Normal convergence of nonlocalised geometric functionals and shot-noise excursions