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On the number of particles from a marked set of cells for an analogue of a general allocation scheme

  • Aleksey N. Chuprunov
Published/Copyright: July 15, 2025

Abstract

In a general scheme of allocation of no more than n particles to N cells we prove limit theorems for the random variable ηn,N(K) which is the number of particles in a given set of K cells. The main result of the paper is Theorem 1. Limit distribution in this theorem depends on s=limKN. If 0 < s < 1, then the limit distribution is that of the minimum of independent Gaussian random variables, and if s = 1, then it is the distribution of the absolute value of a Gaussian random variable taken with the minus sign.


Originally published in Diskretnaya Matematika (2023) 35, №2, 143–151 (in Russian).


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Received: 2022-07-29
Published Online: 2025-07-15
Published in Print: 2025-06-26

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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