caa a22 4500 605524548 CHVBK 20210128100754.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10958-015-2299-3 doi (NATIONALLICENCE)springer-10.1007/s10958-015-2299-3 Estimates for the Concentration Functions in the Littlewood-Offord Problem [Elektronische Daten] [Yu. Eliseeva, F. Götze, A. Zaitsev] Let X,X1, . . . , Xn be independent, identically distributed random variables. In this paper, we study the behavior of concentration functions of the weighted sums ∑ k = 1 n a k X k $$ {\displaystyle \sum_{k=1}^n{a}_k{X}_k} $$ with respect to the arithmetic structure of coefficients ak. Such concentration results recently became important in connection with the study of singular values of random matrices. In this paper, we formulate and prove some refinements of a result of Vershynin (2014). Springer Science+Business Media New York, 2015 Eliseeva Yu St. Petersburg State University, St. Petersburg, Russia aut Götze F. Bielefeld University, Bielefeld, Germany aut Zaitsev A. St. Petersburg Department of the Steklov Mathematical Institute and St. Petersburg State University, St. Petersburg, Russia aut Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 206/2(2015-04-01), 146-158 1072-3374 206:2<146 2015 206 10958 https://doi.org/10.1007/s10958-015-2299-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2299-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Eliseeva Yu St. Petersburg State University, St. Petersburg, Russia aut NATIONALLICENCE 700 1- Götze F. Bielefeld University, Bielefeld, Germany aut NATIONALLICENCE 700 1- Zaitsev A. St. Petersburg Department of the Steklov Mathematical Institute and St. Petersburg State University, St. Petersburg, Russia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 206/2(2015-04-01), 146-158 1072-3374 206:2<146 2015 206 10958