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A New Bound in the Littlewood–Offord Problem. / Götze, Friedrich; Zaitsev, Andrei Yu.

In: Mathematics, Vol. 10, No. 10, 1740, 19.05.2022.

Research output: Contribution to journal › Article › peer-review

Harvard

Götze, F & Zaitsev, AY 2022, 'A New Bound in the Littlewood–Offord Problem', Mathematics, vol. 10, no. 10, 1740. https://doi.org/10.3390/math10101740

APA

Götze, F., & Zaitsev, A. Y. (2022). A New Bound in the Littlewood–Offord Problem. Mathematics, 10(10), [1740]. https://doi.org/10.3390/math10101740

Vancouver

Götze F, Zaitsev AY. A New Bound in the Littlewood–Offord Problem. Mathematics. 2022 May 19;10(10). 1740. https://doi.org/10.3390/math10101740

Author

Götze, Friedrich ; Zaitsev, Andrei Yu. / A New Bound in the Littlewood–Offord Problem. In: Mathematics. 2022 ; Vol. 10, No. 10.

BibTeX

@article{27a065c7eb9b41a4923f2cebb38b59af,
title = "A New Bound in the Littlewood–Offord Problem",
abstract = "The paper deals with studying a connection of the Littlewood–Offord problem with estimating the concentration functions of some symmetric infinitely divisible distributions. It is shown that the concentration function of a weighted sum of independent identically distributed random variables is estimated in terms of the concentration function of a symmetric infinitely divisible distribution whose spectral measure is concentrated on the set of plus-minus weights.",
keywords = "concentration functions, inequalities, sums of independent random variables, the Littlewood–Offord problem, функции концентрации, неравенства, проблема Литтлвуда–Оффорда, суммы независимых случайных величин.",
author = "Friedrich G{\"o}tze and Zaitsev, {Andrei Yu}",
note = "Publisher Copyright: {\textcopyright} 2022 by the authors. Licensee MDPI, Basel, Switzerland.",
year = "2022",
month = may,
day = "19",
doi = "10.3390/math10101740",
language = "English",
volume = "10",
journal = "Mathematics",
issn = "2227-7390",
publisher = "MDPI AG",
number = "10",

}

RIS

TY - JOUR

T1 - A New Bound in the Littlewood–Offord Problem

AU - Götze, Friedrich

AU - Zaitsev, Andrei Yu

N1 - Publisher Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2022/5/19

Y1 - 2022/5/19

N2 - The paper deals with studying a connection of the Littlewood–Offord problem with estimating the concentration functions of some symmetric infinitely divisible distributions. It is shown that the concentration function of a weighted sum of independent identically distributed random variables is estimated in terms of the concentration function of a symmetric infinitely divisible distribution whose spectral measure is concentrated on the set of plus-minus weights.

AB - The paper deals with studying a connection of the Littlewood–Offord problem with estimating the concentration functions of some symmetric infinitely divisible distributions. It is shown that the concentration function of a weighted sum of independent identically distributed random variables is estimated in terms of the concentration function of a symmetric infinitely divisible distribution whose spectral measure is concentrated on the set of plus-minus weights.

KW - concentration functions

KW - inequalities

KW - sums of independent random variables

KW - the Littlewood–Offord problem

KW - функции концентрации, неравенства, проблема Литтлвуда–Оффорда, суммы независимых случайных величин.

UR - http://www.scopus.com/inward/record.url?scp=85130906458&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/5ff207fd-f559-3e42-bd9b-f8fb49eb7f66/

U2 - 10.3390/math10101740

DO - 10.3390/math10101740

M3 - Article

AN - SCOPUS:85130906458

VL - 10

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 10

M1 - 1740

ER -

ID: 100912067