ARAK INEQUALITIES FOR CONCENTRATION FUNCTIONS AND THE LITTLEWOOD-OFFORD PROBLEM

Götze F, Eliseeva YS, Zaitsev AY (2018)
THEORY OF PROBABILITY AND ITS APPLICATIONS 62(2): 196-215.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Götze, FriedrichUniBi; Eliseeva, Yu S.; Zaitsev, A. Yu
Abstract / Bemerkung
Let X,X-1,..., X-n be independent identically distributed random variables. In this paper we study the behavior of the concentration functions of the weighted sums Sigma(n)(k=1) X(k)a(k) depending on the arithmetic structure of the coefficients a(k). The results obtained the last 10 years for the concentration functions of weighted sums play an important role in the study of singular numbers of random matrices. Recently, Tao and Vu proposed a so-called inverse principle for the Littlewood-Offord problem. We discuss the relations between this inverse principle and a similar principle for sums of arbitrarily distributed independent random variables formulated by Arak in the 1980s.
Stichworte
concentration functions; inequalities; the Littlewood-Offord problem; sums of independent random variables
Erscheinungsjahr
2018
Zeitschriftentitel
THEORY OF PROBABILITY AND ITS APPLICATIONS
Band
62
Ausgabe
2
Seite(n)
196-215
ISSN
0040-585X
eISSN
1095-7219
Page URI
https://pub.uni-bielefeld.de/record/2920708

Zitieren

Götze F, Eliseeva YS, Zaitsev AY. ARAK INEQUALITIES FOR CONCENTRATION FUNCTIONS AND THE LITTLEWOOD-OFFORD PROBLEM. THEORY OF PROBABILITY AND ITS APPLICATIONS. 2018;62(2):196-215.
Götze, F., Eliseeva, Y. S., & Zaitsev, A. Y. (2018). ARAK INEQUALITIES FOR CONCENTRATION FUNCTIONS AND THE LITTLEWOOD-OFFORD PROBLEM. THEORY OF PROBABILITY AND ITS APPLICATIONS, 62(2), 196-215. doi:10.1137/S0040585X97T988563
Götze, F., Eliseeva, Y. S., and Zaitsev, A. Y. (2018). ARAK INEQUALITIES FOR CONCENTRATION FUNCTIONS AND THE LITTLEWOOD-OFFORD PROBLEM. THEORY OF PROBABILITY AND ITS APPLICATIONS 62, 196-215.
Götze, F., Eliseeva, Y.S., & Zaitsev, A.Y., 2018. ARAK INEQUALITIES FOR CONCENTRATION FUNCTIONS AND THE LITTLEWOOD-OFFORD PROBLEM. THEORY OF PROBABILITY AND ITS APPLICATIONS, 62(2), p 196-215.
F. Götze, Y.S. Eliseeva, and A.Y. Zaitsev, “ARAK INEQUALITIES FOR CONCENTRATION FUNCTIONS AND THE LITTLEWOOD-OFFORD PROBLEM”, THEORY OF PROBABILITY AND ITS APPLICATIONS, vol. 62, 2018, pp. 196-215.
Götze, F., Eliseeva, Y.S., Zaitsev, A.Y.: ARAK INEQUALITIES FOR CONCENTRATION FUNCTIONS AND THE LITTLEWOOD-OFFORD PROBLEM. THEORY OF PROBABILITY AND ITS APPLICATIONS. 62, 196-215 (2018).
Götze, Friedrich, Eliseeva, Yu S., and Zaitsev, A. Yu. “ARAK INEQUALITIES FOR CONCENTRATION FUNCTIONS AND THE LITTLEWOOD-OFFORD PROBLEM”. THEORY OF PROBABILITY AND ITS APPLICATIONS 62.2 (2018): 196-215.