A New Bound in the Littlewood–Offord Problem

Friedrich Götze and Andrei Yu. Zaitsev
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Friedrich Götze: Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
Andrei Yu. Zaitsev: St. Petersburg Department of Steklov Mathematical Institute, Fontanka 27, St. Petersburg 191023, Russia

Mathematics, 2022, vol. 10, issue 10, 1-6

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; the Littlewood–Offord problem; sums of independent random variables (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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