Moderate deviations for some point measures in geometric probability

Abstract

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.

Published in at http://dx.doi.org/10.1214/07-AIHP137 the Annales de l'Institut Henri Poincaré - Probabilités et Statistiques (http://www.imstat.org/aihp/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (5)

• Gaussian limits for random measures in geometric probability
• Perfect simulation for interacting point processes, loss networks and Ising models
• Laws of large numbers in stochastic geometry with statistical applications
• Variance asymptotics and central limit theorems for generalized growth processes with applications to convex hulls and maximal points
• Loss network representation of Peierls contours

Cited by in corpus (4)

• Gaussian limits for random measures in geometric probability
• Limit theory for geometric statistics of point processes having fast decay of correlations
• Moderate deviations for stabilizing functionals in geometric probability
• Corrected mean-field model for random sequential adsorption on random geometric graphs