Geodesic
Limit distributions of the maximal distance to the nearest neighbour
Diskretnaya Matematika, Tome 30 (2018) no. 3, pp. 88-98.

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For sets of iid random points having a uniform (in a definite sense) distribution on the arbitrary metric space a maximal distance to the nearest neighbour is considered. By means of the Chen–Stein method new limit theorems for this random variable is proved. For random uniform samples from the set of binary cube vertices analogous results are obtained by the methods of moments.
Keywords: random points in a metric space, maximal distance to the nearest neighbour, limit distributions, binary cube. 
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O. P. Orlov. Limit distributions of the maximal distance to the nearest neighbour. Diskretnaya Matematika, Tome 30 (2018) no. 3, pp. 88-98. http://geodesic.mathdoc.fr/item/DM_2018_30_3_a7/

[1] Barbour A. D., Chen Louis H. Y., An introduction to Stein's method, Singapore University Press and World Scientific Publishing Co. Pte. Ltd, 2005 | MR | Zbl

[2] Barbour A. D., Holst Lars, Janson Svante, Poisson approximation, Clarendon press, Oxford, 1992 | MR | Zbl

[3] Zubkov A. M., Orlov O. P., “Predelnye raspredeleniya ekstremalnykh rasstoyanii do blizhaishego soseda”, Diskretnaya matematika, 29:2 (2017), 3–17 ; Zubkov A. M., Orlov O. P., “Limit distributions of extremal distances to the nearest neighbor”, Discrete Math. Appl., 28:3 (2018), 189–199 | DOI | MR | DOI | MR

[4] Hoeffding Wassily, “Probability inequalities for sums of bounded random variables”, J. Amer. Stat. Assoc., 58:301 (1963), 13–30 | DOI | MR | Zbl

[5] Henze Norbert, “The limit distribution for maxima of “weighted” rth-nearest-neighbour distances”, J. Appl. Probab., 19:2 (1982), 344–354 | DOI | MR | Zbl