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.
Publié le : 2008-06-15
Classification:
Moderate deviations,
Laws of the iterated logarithm,
Random Euclidean graphs,
Random sequential packing,
60F05,
60D05
@article{1211819419,
author = {Baryshnikov, Yu and Eichelsbacher, P. and Schreiber, T. and Yukich, J. E.},
title = {Moderate deviations for some point measures in geometric probability},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {44},
number = {2},
year = {2008},
pages = { 422-446},
language = {en},
url = {http://dml.mathdoc.fr/item/1211819419}
}
Baryshnikov, Yu; Eichelsbacher, P.; Schreiber, T.; Yukich, J. E. Moderate deviations for some point measures in geometric probability. Ann. Inst. H. Poincaré Probab. Statist., Tome 44 (2008) no. 2, pp. 422-446. http://gdmltest.u-ga.fr/item/1211819419/