Normal Approximation in Geometric Probability

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. 1 Department of Mathematical Sciences, University of Bath, Bath BA1 7AY, United Kingdom: [email protected] 2 Department of Mathematics, Lehigh University, Bethlehem PA 18015: [email protected] 2 Research supported in part by NSA grant MDA904-01-1-0029 and NSF grant DMS-0203720