Moderate deviations for some point measures in geometric probability

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

Annales de l'I.H.P. Probabilités et statistiques, Tome 44 (2008) no. 3, pp. 422-446.

Les fonctionnelles en probabilite géométrique s’expriment souvent comme des sommes de fonctions bornées qui possèdent la fonction de stabilisation. Les méthodes de cumulants et les modifications exponentielles des mesures démontrent que ces fonctionnelles vérifient le principe des déviations modérées. Ceci donne des principes des déviations modérées et des lois de logarithme itéré pour des modèles de ‘packing aléatoires’ ainsi que pour des statistiques de modèles de ‘germe-grain’ et de graphes avec $k$ plus proches voisins.

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.

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