Moderate deviations for stabilizing functionals in geometric probability

Details Moderate deviations for stabilizing functionals in geometric probability Moderate deviations for stabilizing functionals in geometric probability

2010-10-08

arxiv.org/abs/1010.1665v1

Mathematics

Probability

20 pages

Scientific paper

The purpose of the present paper is to establish explicit bounds on moderate deviation probabilities for a rather general class of bounded geometric functionals enjoying the exponential stabilization property. Compared to our previous work, the price to pay for the considerably larger generality of our estimates is a narrower scale range in which our moderate deviation results hold; we argue that a range limitation seems inevitable under our general assumptions though. Our proof techniques rely on cumulant expansions and cluster measures and yield completely explicit bounds on deviation probabilities. The examples of geometric functionals we treat include bounded statistics of random packing models and random graphs arising in computational geometry, such as Euclidean nearest neighbor graphs, Voronoi graphs and sphere of influence graphs.

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