Bounds for the Rate of Convergence in the Generalized Rényi Theorem [PDF]
Mathematics, 2022 In the paper, an overview is presented of the results on the convergence rate bounds in limit theorems concerning geometric random sums and their generalizations to mixed Poisson random sums, including the case where the mixing law is itself a mixed ...
Victor Korolev
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Mathematics, 2023 This paper considers a generalization of the Rényi theorem to the case of a structural distribution with a scale parameter. In terms of the zeta metric, some estimates of the convergence rate in the generalized Rényi theorem are obtained when the ...
Alexey Kudryavtsev, Oleg Shestakov
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A Rényi-Type Limit Theorem on Random Sums and the Accuracy of Likelihood-Based Classification of Random Sequences with Application to Genomics [PDF]
Mathematics, 2023 We study classification of random sequences of characters selected from a given alphabet into two classes characterized by distinct character selection probabilities and length distributions.
Leonid Hanin, Lyudmila Pavlova
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Generalized Rényi Entropy Accumulation Theorem and Generalized Quantum Probability Estimation
Physical Review XThe entropy accumulation theorem—and its subsequent generalized version—is a powerful tool in the security analysis of many device-dependent and device-independent cryptography protocols. However, it has the drawback that the finite-size bounds it yields
Amir Arqand +2 more
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A Generalized Equilibrium Transform with Application to Error Bounds in the Rényi Theorem with No Support Constraints [PDF]
Mathematics, 2020 We introduce a generalized stationary renewal distribution (also called the equilibrium transform) for arbitrary distributions with finite nonzero first moment and study its properties.
Irina Shevtsova, Mikhail Tselishchev
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Sharp Estimates for Proximity of Geometric and Related Sums Distributions to Limit Laws
Mathematics, 2022 The convergence rate in the famous Rényi theorem is studied by means of the Stein method refinement. Namely, it is demonstrated that the new estimate of the convergence rate of the normalized geometric sums to exponential law involving the ideal ...
Alexander Bulinski, Nikolay Slepov
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Mathematics, 2021 We investigate the efficiency of several types of continued fraction expansions of a number in the unit interval using a generalization of Lochs theorem from 1964.
Dan Lascu, Gabriela Ileana Sebe
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Central limit theorem for the principal eigenvalue and eigenvector of Chung–Lu random graphs
Journal of Physics: Complexity, 2023 A Chung–Lu random graph is an inhomogeneous Erdős–Rényi random graph in which vertices are assigned average degrees, and pairs of vertices are connected by an edge with a probability that is proportional to the product of their average degrees ...
Pierfrancesco Dionigi +4 more
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On the Accuracy of the Generalized Gamma Approximation to Generalized Negative Binomial Random Sums
Mathematics, 2021 We investigate the proximity in terms of zeta-structured metrics of generalized negative binomial random sums to generalized gamma distribution with the corresponding parameters, extending thus the zeta-structured estimates of the rate of convergence in ...
Irina Shevtsova, Mikhail Tselishchev
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Thermodynamics of exponential Kolmogorov–Nagumo averages
New Journal of Physics, 2023 This paper investigates generalized thermodynamic relationships in physical systems where relevant macroscopic variables are determined by the exponential Kolmogorov–Nagumo average.
Pablo A Morales +2 more
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