New applications of Arak's inequalities to the Littlewood-Offord problem

Götze F, Zaitsev AY (2018)
EUROPEAN JOURNAL OF MATHEMATICS 4(2): 639-663.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Götze, FriedrichUniBi; Zaitsev, Andrei Yu.
Abstract / Bemerkung
Let X-1, . . . , X-n be independent identically distributed random variables. In this paper we study the behavior of concentration functions of weighted sums Sigma(n)(k=1) X(k)a(k) with respect to the arithmetic structure of coefficients a(k) in the context of the Littlewood-Offord problem. In recent papers of Eliseeva, Gotze and Zaitsev, we discussed the relations between the inverse principles stated by Nguyen, Tao and Vu and similar principles formulated by Arak in his papers from the 1980's. In this paper, we will derive some more general and more precise consequences of Arak's inequalities providing new results in the Littlewood-Offord problem.
Stichworte
Concentration functions; Inequalities; Littlewood-Offord problem; Sums; of independent random variables
Erscheinungsjahr
2018
Zeitschriftentitel
EUROPEAN JOURNAL OF MATHEMATICS
Band
4
Ausgabe
2
Seite(n)
639-663
ISSN
2199-675X
eISSN
2199-6768
Page URI
https://pub.uni-bielefeld.de/record/2930279

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Götze F, Zaitsev AY. New applications of Arak's inequalities to the Littlewood-Offord problem. EUROPEAN JOURNAL OF MATHEMATICS. 2018;4(2):639-663.
Götze, F., & Zaitsev, A. Y. (2018). New applications of Arak's inequalities to the Littlewood-Offord problem. EUROPEAN JOURNAL OF MATHEMATICS, 4(2), 639-663. doi:10.1007/s40879-018-0215-3
Götze, F., and Zaitsev, A. Y. (2018). New applications of Arak's inequalities to the Littlewood-Offord problem. EUROPEAN JOURNAL OF MATHEMATICS 4, 639-663.
Götze, F., & Zaitsev, A.Y., 2018. New applications of Arak's inequalities to the Littlewood-Offord problem. EUROPEAN JOURNAL OF MATHEMATICS, 4(2), p 639-663.
F. Götze and A.Y. Zaitsev, “New applications of Arak's inequalities to the Littlewood-Offord problem”, EUROPEAN JOURNAL OF MATHEMATICS, vol. 4, 2018, pp. 639-663.
Götze, F., Zaitsev, A.Y.: New applications of Arak's inequalities to the Littlewood-Offord problem. EUROPEAN JOURNAL OF MATHEMATICS. 4, 639-663 (2018).
Götze, Friedrich, and Zaitsev, Andrei Yu. “New applications of Arak's inequalities to the Littlewood-Offord problem”. EUROPEAN JOURNAL OF MATHEMATICS 4.2 (2018): 639-663.