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Quantum entropy and central limit theorem [PDF]
Proceedings of the National Academy of Sciences of the United States of America, 2023 We introduce a framework to study discrete-variable (DV) quantum systems based on qudits. It relies on notions of a mean state (MS), a minimal stabilizer-projection state (MSPS), and a new convolution. Some interesting consequences are: The MS is the closest MSPS to a given state with respect to the relative entropy; the MS is extremal with respect to ...
Kaifeng Bu, Arthur Jaffé
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Central limit theorem: the cornerstone of modern statistics [PDF]
Korean Journal of Anesthesiology, 2017 According to the central limit theorem, the means of a random sample of size, n, from a population with mean, µ, and variance, σ2, distribute normally with mean, µ, and variance, σ2n.
Sang Gyu Kwak, Jong Hae Kim
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Accuracy and Precision Improvement of Temperature Measurement Using Statistical Analysis/Central Limit Theorem [PDF]
Sensors, 2023 This paper describes a method for increasing the accuracy and precision of temperature measurements of a liquid based on the central limit theorem. A thermometer immersed in a liquid exhibits a response with determined accuracy and precision.
Francisco Antônio Belo +4 more
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Entropy and the Central Limit Theorem
Annals of Probability, 1986 The author establishes a strengthened central limit theorem for densities showing monotone convergence in the sense of relative entropy. The relative entropy is defined by \[ D_ n=\int f(x) \log f(x)/\phi (x)dx \] where f is the density function of a random variable, X, with finite variance and \(\phi\) is the normal density with the same mean and ...
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Conditions of the Central-Limit Theorem Are Rarely Satisfied in Empirical Psychological Studies [PDF]
Frontiers in Psychology, 2021 Tadamasa Sawada
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Central Limit Theorem in View of Subspace Convex-Cyclic Operators [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2021 In our work we have defined an operator called subspace convex-cyclic operator. The property of this newly defined operator relates eigenvalues which have eigenvectors of modulus one with kernels of the operator.
H.M. Hasan +3 more
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A Central Limit Theorem for Predictive Distributions
Mathematics, 2021 Let S be a Borel subset of a Polish space and F the set of bounded Borel functions f:S→R. Let an(·)=P(Xn+1∈·∣X1,…,Xn) be the n-th predictive distribution corresponding to a sequence (Xn) of S-valued random variables.
Patrizia Berti +2 more
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Central limit theorem in the symmetric group
Lietuvos Matematikos Rinkinys, 1999 In this work we investigate a rate of convergence of sums of random variables defined on a symetric group Sn, when the probability measure on Sn is defined by the Ewens sampling formula with parameter θ. Using the results obtained by E.
Vytas Zacharovas
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A Central Limit Theorem for Vincular Permutation Patterns [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 We study the number of occurrences of any fixed vincular permutation pattern. We show that this statistics on uniform random permutations is asymptotically normal and describe the speed of convergence.
Lisa Hofer
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Holderian functional central limit theorem for linear processes
Lietuvos Matematikos Rinkinys, 2004 Let (Xt)t ≥ 1 be a linear process defined by Xt = ∑i=0∞ψi εt-1 where (ψi, i ≥ 0) is a sequence of real numbers and (εi , i ∈ Z) is a sequence of random variables with null expectation and variance 1.
Mindaugas Juodis
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