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On a Functional of the Number of Nonoverlapping Chains Appearing in the Polynomial Scheme and Its Connection with Entropy

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Abstract

Consider \(n\) independent chains consisting of \(k\) independent polynomial trials with \(M\) outcomes. It is assumed that \(n, k \to \infty\) and \(\ln(n/M^k)=o(k)\). We find the asymptotics of the normalized logarithm of the number of appearing chains and indicate the connection between this functional and the entropy.

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Acknowledgments

The author wishes to express gratitude to A. M. Zubkov for the statement of the problem and for valuable advice.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119234, Russia

    M. P. Savelov

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  1. M. P. Savelov
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Correspondence to M. P. Savelov.

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Translated from Matematicheskie Zametki, 2023, Vol. 114, pp. 390–403 https://doi.org/10.4213/mzm13868.

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Savelov, M.P. On a Functional of the Number of Nonoverlapping Chains Appearing in the Polynomial Scheme and Its Connection with Entropy. Math Notes 114, 339–350 (2023). https://doi.org/10.1134/S0001434623090067

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  • DOI: https://doi.org/10.1134/S0001434623090067

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