Normal Approximation in Geometric Probability

By Mathew D. Penrose, Joseph E. Yukich. 2004

101 citations recorded by the source corpus.

We use Stein’s method to obtain bounds on the rate of convergence for a class of statistics in geometric probability obtained as a sum of contributions from Poisson points which are exponentially stabilizing, i.e. locally determined in a certain sense. Examples include statistics such as total edge length and total number of edges of graphs in computational geometry and the total number of particles accepted in random sequential packing models. These rates also apply to the 1-dimensional marginals of the random measures associated with these statistics.

Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ab0d75729114e8bb33d4c3204c33a22dd4c537b5

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In Applied Mathematics

In Discrete Mathematics and Combinatorics

In Statistics and Probability

Citations in the corpus

Lectures on the Poisson Process (2017, background): “Many Poisson functionals arising in stochastic geometry have a property of stabilisation (local dependence); central limit and normal approximation theorems based on this property have been established in [128, 130, 131].”
Normal approximation on Poisson spaces: Mehler’s formula, second order Poincaré inequalities and stabilization (2014, methodology): “Central limit theorems for the total edge length of the k-nearest neighbour graph were studied in [3, 5, 6, 40, 42, 44].”
Gaussian Limts for Random Geometric Measures (2007, methodology): “Recently, attention has turned to the asymptotic behaviour of the measure itself (rather than only its total measure), notably in (3; 11; 18; 19; 24; 25).”
Fine Gaussian fluctuations on the Poisson space, I: contractions, cumulants and geometric random graphs (2011, background): “The CLTs presented for instance in [1, 30] cover well this case.”