Moderate deviations for some point measures in geometric probability

DOI10.1214/07-AIHP137zbMath1175.60015arXivmath/0603022OpenAlexW3103532859MaRDI QIDQ731680

Joseph E. Yukich, Tomasz Schreiber, Yu. Baryshnikov, Peter Eichelsbacher

Publication date: 8 October 2009

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0603022

zbMATH Keywords

moderate deviationslaws of the iterated logarithmrandom Euclidean graphsrandom sequential packing

Mathematics Subject Classification ID

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

Related Items

Large deviations for functionals of spatial point processes with applications to random packing and spatial graphs ⋮ Limit Theorems in Discrete Stochastic Geometry ⋮ Limit behaviors of random connected graphs driven by a Poisson process ⋮ Corrected mean-field model for random sequential adsorption on random geometric graphs ⋮ Moderate deviations for stabilizing functionals in geometric probability ⋮ Gaussian limits for random measures in geometric probability ⋮ Process level moderate deviations for stabilizing functionals ⋮ The law of the iterated logarithm for sums of exponentially stabilizing functionals ⋮ Parametric Modeling of Sparse Random Trees Using 3D Copulas

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Perfect simulation for marked point processes
• An introduction to the theory of point processes
• Packing random intervals on-line
• Domination by product measures
• Central limit theory for the number of seeds in a growth model in \(\mathbb{R}^ d\) with inhomogeneous Poisson arrivals
• Rank-dependent moderate deviations of \(U\)-empirical measures in strong topologies
• Gaussian limits for random measures in geometric probability
• Large deviations of \(U\)-empirical measures in strong topologies and applications
• Gaussian fields and random packing
• Loss network representation of Peierls contours
• Weak laws of large numbers in geometric probability
• Limit theory for random sequential packing and deposition
• Central limit theorems for some graphs in computational geometry.
• Gaussian limits for random geometric measures
• Variance asymptotics and central limit theorems for generalized growth processes with applications to convex hulls and maximal points
• Laws of large numbers in stochastic geometry with statistical applications
• Multivariate spatial central limit theorems with applications to percolation and spatial graphs
• Perfect simulation for interacting point processes, loss networks and Ising models.
• Central limit theorem for germination-growth models in ℝ^d with non-Poisson locations
• Random Geometric Graphs
• Central limit theorem for a class of random measures associated with germ-grain models
• Normal approximation for random sums