The paper deals with studying a connection between the Littlewood–Offord problem and estimating the concentration functions of some symmetric infinitely divisible distributions. Some multivariate generalizations of Arak’s results (1980) are given. They establish a relationship of the concentration function of the sum and arithmetic structure of supports of the distributions of independent random vectors for arbitrary distributions of summands. Bibliography: 21 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 431, 2014, pp. 72–81.
Translated by A. Yu. Zaitsev.
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Eliseeva, Y.S., Zaitsev, A.Y. On the Littlewood–Offord Problem. J Math Sci 214, 467–473 (2016). https://doi.org/10.1007/s10958-016-2790-5
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DOI: https://doi.org/10.1007/s10958-016-2790-5