Moderate deviations for some point measures in geometric probability

Yu Baryshnikov, P. Eichelsbacher, T. Schreiber, J. E. Yukich

Published 2006-03-01, updated 2008-06-18Version 4

Functionals in geometric probability are often expressed as sums of bounded functions exhibiting exponential stabilization. Methods based on cumulant techniques and exponential modifications of measures show that such functionals satisfy moderate deviation principles. This leads to moderate deviation principles and laws of the iterated logarithm for random packing models as well as for statistics associated with germ-grain models and $k$ nearest neighbor graphs.