Geodesic
Asymptotic normality of symmetric decomposable statistics in an inhomogeneous scheme
Diskretnaya Matematika, Tome 1 (1989) no. 2, pp. 15-27

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Sufficient conditions for the asymptotic normality of one-dimensional and multi-dimensional symmetric decomposable statistics in an inhomogeneous scheme (independent of the position of the particle with a denumerable set of cells) are given. The proofs are based on the approximation of symmetric decomposable statistics by $U$-statistics. 
@article{DM_1989_1_2_a1,
     author = {V. G. Mikhailov},
     title = {Asymptotic normality of symmetric decomposable statistics in an inhomogeneous scheme},
     journal = {Diskretnaya Matematika},
     pages = {15--27},
     publisher = {mathdoc},
     volume = {1},
     number = {2},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1989_1_2_a1/}
}
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V. G. Mikhailov. Asymptotic normality of symmetric decomposable statistics in an inhomogeneous scheme. Diskretnaya Matematika, Tome 1 (1989) no. 2, pp. 15-27. http://geodesic.mathdoc.fr/item/DM_1989_1_2_a1/