Geodesic
The Law of the Iterated Logarithm for Sums of Exponentially Stabilizing Functionals
Matematičeskie zametki, Tome 85 (2009) no. 2, pp. 234-245

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We consider sums of exponentially stabilizing functionals (introduced by Penrose and Yukich) of Poisson point processes in $d$-dimensional Euclidean space. The asymptotic behavior of such sums is studied in terms of a random field (defined on the lattice $\mathbb Z^d$) each element of which is a certain sum of functionals with respect to the corresponding unit cube in $\mathbb R^d$. For this random field, we obtain an exponential estimate of the decrease of the strong mixing coefficient and establish the law of the iterated logarithm.
Keywords: law of the iterated logarithm, random field, exponentially stabilizing functional, strong mixing coefficient.
Mots-clés : Poisson point process 
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     author = {M. M. Musin},
     title = {The {Law} of the {Iterated} {Logarithm} for {Sums} of {Exponentially} {Stabilizing} {Functionals}},
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M. M. Musin. The Law of the Iterated Logarithm for Sums of Exponentially Stabilizing Functionals. Matematičeskie zametki, Tome 85 (2009) no. 2, pp. 234-245. http://geodesic.mathdoc.fr/item/MZM_2009_85_2_a6/