Normal Approximation in Geometric Probability
By Mathew D. Penrose and J.E. Yukich
Statistics arising in geometric probability can often be
expressed as sums of stabilizing functionals, that is functionals
which satisfy a local dependence structure.
In this note we show that stabilization
leads to nearly optimal rates of convergence in the CLT for
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.