随机等概率分配方案中空单元数的局部极限定理

IF 0.3 Q4 MATHEMATICS, APPLIED

Discrete Mathematics and Applications Pub Date : 2023-02-01 DOI:10.1515/dma-2023-0004

O. P. Orlov

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引用次数: 0

摘要

摘要考虑了一个将n个粒子随机等概率分配到n个单元的经典方案。在n，n的条件下，我们得到了空单元数等于k的概率的一个渐近公式 → ∞ 使得n/（n − k）是有界的，并且从下面与1分离。

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Local limit theorem for the number of empty cells in a scheme of random equiprobable allocations

Abstract A classical scheme of random equiprobable allocations of n particles into N cells is considered. We find an asymptotic formula for the probability that the number of empty cells is equal to k under the condition that n, N → ∞ in such a way that n/(N − k) is bounded and separated from 1 from below.

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来源期刊

Discrete Mathematics and Applications MATHEMATICS, APPLIED-

CiteScore

0.60

自引率

20.00%

发文量

期刊介绍： The aim of this journal is to provide the latest information on the development of discrete mathematics in the former USSR to a world-wide readership. The journal will contain papers from the Russian-language journal Diskretnaya Matematika, the only journal of the Russian Academy of Sciences devoted to this field of mathematics. Discrete Mathematics and Applications will cover various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.