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A New Bound in the Littlewood–Offord Problem

Author

Listed:
  • 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 and Mechanics Faculty, St. Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg 199034, Russia)

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.

Suggested Citation

  • Friedrich Götze & Andrei Yu. Zaitsev, 2022. "A New Bound in the Littlewood–Offord Problem," Mathematics, MDPI, vol. 10(10), pages 1-6, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1740-:d:819114
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