Normal Approximation in Geometric Probability

Details Normal Approximation in Geometric Probability Normal Approximation in Geometric Probability

2004-09-06

arxiv.org/abs/math/0409088v1

Mathematics

Probability

To appear in the proceedings of the Workshop on Stein's Method and Applications, 11-15 August 2003, Institute of Mathematical

Scientific paper

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.

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