Local limit theorem for the number of empty cells in a scheme of random equiprobable allocations
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Oleg P. Orlov
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.
Note
Originally published in Diskretnaya Matematika (2021) 33, №4, 83–93 (in Russian).
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Articles in the same Issue
- Frontmatter
- Some classes of easily testable circuits in the Zhegalkin basis
- On the concentration of the independence numbers of random hypergraphs
- On implementation of some systems of elementary conjunctions in the class of separating contact circuits
- Local limit theorem for the number of empty cells in a scheme of random equiprobable allocations
- Maximally nonlinear functions over finite fields
- The limit joint distributions of statistics of four tests of the NIST package
Articles in the same Issue
- Frontmatter
- Some classes of easily testable circuits in the Zhegalkin basis
- On the concentration of the independence numbers of random hypergraphs
- On implementation of some systems of elementary conjunctions in the class of separating contact circuits
- Local limit theorem for the number of empty cells in a scheme of random equiprobable allocations
- Maximally nonlinear functions over finite fields
- The limit joint distributions of statistics of four tests of the NIST package
