Moderate deviations for some point measures in geometric probability

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

doi:10.1214/07-AIHP137

Moderate deviations for some point measures in geometric probability

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

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

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.

Original language	English
Pages (from-to)	422-446
Number of pages	25
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	44
Issue number	3
DOIs	https://doi.org/10.1214/07-AIHP137
Publication status	Published - Jun 1 2008
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/07-AIHP137

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AB - 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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Moderate deviations for some point measures in geometric probability

Abstract

All Science Journal Classification (ASJC) codes

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