Asymptotics of conditional probabilities of succesful allocation of random number of particles into cells
-
Aleksandra I. Afonina
and
Aleksey N. Chuprunov
Abstract
The article is devoted to the memory of Valentin Fedorovich Kolchin.
Let ζ, ζi (i ∈ N) be independent identically distributed nonnegative integer-valued random variables, (ηi1,…, ηiN) be the fillings of cells in the generalized scheme of allocation of ζi particles into N cells, 1 ≤ i ≤ n, for fixed Zn = (ζ1, …, ζn) these allocation schemes are independent. We consider the conditional probabilities P(An,N | Zn) of the event An,N = {each cell in each of n allocation schemes contains no more than r particles}, where r is some fixed number. The sufficient conditions for the convergence of the sequence P(An,N | Zn) to a nonrandom limit with probability 1 are given. It is shown that the random variable ln P(An,N | Zn) is asymptotically normal. Applications of the obtained results to the noise-proof encoding are discussed.
Originally published in Diskretnaya Matematika (2016) 28,№3, 14–25 (in Russian).
Funding source: Russian Foundation for Basic Research
Award Identifier / Grant number: 14-01-00351
Funding statement: This work was financially supported by the Russian Foundation for Basic Research, project No 14-01-00351, and by the RFBR and the Government of the Republic of Tatarstan, the project No 15-41-02433.
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Articles in the same Issue
- Frontmatter
- Functional limit theorem for a stopped random walk attaining a high level
- Asymptotics of conditional probabilities of succesful allocation of random number of particles into cells
- Lower bound for the complexity of five-valued polarized polynomials
- The minimum number of negations in circuits for systems of multi-valued functions
- Bounded prefix concatenation operation and finite bases with respect to the superposition
- On the number of maximal independent sets in complete q-ary trees
- Lower estimate for the cardinality of the domain of universal functions for the class of linear Boolean functions
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Articles in the same Issue
- Frontmatter
- Functional limit theorem for a stopped random walk attaining a high level
- Asymptotics of conditional probabilities of succesful allocation of random number of particles into cells
- Lower bound for the complexity of five-valued polarized polynomials
- The minimum number of negations in circuits for systems of multi-valued functions
- Bounded prefix concatenation operation and finite bases with respect to the superposition
- On the number of maximal independent sets in complete q-ary trees
- Lower estimate for the cardinality of the domain of universal functions for the class of linear Boolean functions
- Limit theorems for the logarithm of the order of a random A-mapping
