Quantitative two-scale stabilization on the Poisson space

DOI10.1214/21-AAP1768zbMath1498.60092arXiv2010.13362OpenAlexW4293483928MaRDI QIDQ2083276

Xiaochuan Yang, Giovanni Peccati, Raphael Lachieze-Rey

Publication date: 10 October 2022

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

Full work available at URL: https://arxiv.org/abs/2010.13362

zbMATH Keywords

excursionsstabilizationMalliavin calculusStein's methodstochastic geometrycentral limit theoremKolmogorov distancePoisson processWasserstein distanceshot noise random fieldsrandom geometric graphsminimal spanning treeconvex distanceMehler's formulaon-line nearest neighbour graph

Mathematics Subject Classification ID

Random fields (60G60) Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Stochastic calculus of variations and the Malliavin calculus (60H07) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (4)

Variance asymptotics and central limit theory for geometric functionals of Poisson cylinder processes ⋮ Rates of multivariate normal approximation for statistics in geometric probability ⋮ Bootstrapping persistent Betti numbers and other stabilizing statistics ⋮ Vector-valued statistics of binomial processes: Berry-Esseen bounds in the convex distance

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Normal approximation of Poisson functionals in Kolmogorov distance
• Central limit theorems for the excursion set volumes of weakly dependent random fields
• Random geometric complexes in the thermodynamic regime
• Multi-dimensional Gaussian fluctuations on the Poisson space
• Poisson process Fock space representation, chaos expansion and covariance inequalities
• Normal approximation on Poisson spaces: Mehler's formula, second order Poincaré inequalities and stabilization
• On the rate of convergence in the multivariate CLT
• A new method of normal approximation
• Stein's method and normal approximation of Poisson functionals
• Asymptotic theory for the multidimensional random on-line nearest-neighbour graph
• Growth rates of Euclidean minimal spanning trees with power weighted edges
• Stein's method for diffusion approximations
• Cost of sequential connection for points in space
• Asymptotics for Euclidean minimal spanning trees on random points
• The central limit theorem for Euclidean minimal spanning trees. I
• Probability theory of classical Euclidean optimization problems
• The fourth moment theorem on the Poisson space
• New Berry-Esseen bounds for functionals of binomial point processes
• Lipschitz-Killing curvatures of excursion sets for two-dimensional random fields
• Berry-Esseen bounds of normal and nonnormal approximation for unbounded exchangeable pairs
• Normal approximation for stabilizing functionals
• Gaussian limits for random measures in geometric probability
• The RSW theorem for continuum percolation and the CLT for Euclidean minimal spanning trees
• The central limit theorem for weighted minimal spanning trees on random points
• Limit theory for random sequential packing and deposition
• Central limit theorems for some graphs in computational geometry.
• Crossings of smooth shot noise processes
• Multivariate normal approximation on the Wiener space: new bounds in the convex distance
• Percolation of the excursion sets of planar symmetric shot noise fields
• Multivariate second order Poincaré inequalities for Poisson functionals
• Normal convergence of nonlocalised geometric functionals and shot-noise excursions
• Minimal spanning trees and Stein's method
• The radial spanning tree of a Poisson point process
• Gaussian limits for multidimensional random sequential packing at saturation
• New Berry-Esseen bounds for non-linear functionals of Poisson random measures
• Multivariate spatial central limit theorems with applications to percolation and spatial graphs
• Normal Approximations with Malliavin Calculus
• Central limit theorems for the radial spanning tree
• Normal Approximation by Stein’s Method
• Explicit laws of large numbers for random nearest-neighbour-type graphs
• Level Sets and Extrema of Random Processes and Fields
• Random Geometric Graphs
• Multiscale functional inequalities in probability: Concentration properties
• Stochastic Geometry and Wireless Networks: Volume I Theory
• Phase Transitions for Random Geometric Preferential Attachment Graphs
• Random Fields and Geometry
• Lectures on the Poisson Process
• Limit theory for the random on‐line nearest‐neighbor graph
• The Malliavin–Stein Method on the Poisson Space
• Stochastic Analysis for Poisson Processes

This page was built for publication: Quantitative two-scale stabilization on the Poisson space