On the inequalities of Erdös-Turán and Berry-Esseen, I
نویسندگان
چکیده
منابع مشابه
Analytic Erdös-Turán conjectures and Erdös-Fuchs theorem
We consider and study formal power series, that we call supported series, with real coefficients which are either zero or bounded below by some positive constant. The sequences of such coefficients have a lot of similarity with sequences of natural numbers considered in additive number theory. It is this analogy that we pursue, thus establishing many properties and giving equivalent statements ...
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The Erdős-Turán law gives a normal approximation for the order of a randomly chosen permutation of n objects. In this paper, we provide a sharp error estimate for the approximation, showing that, if the mean of the approximating normal distribution is slightly adjusted, the error is of order log−1/2n. Combinatorics, Probability and Computing (1994) 3, 167-176 Copyright
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For sum of independent and identically distributed (i.i.d.) random variables {Xi}i=1, the Berry-Esseen theorem states that sup y∈< ∣∣∣∣Pr { 1 sn (X1 + X2 + · · ·+ Xn) ≤ y } − Φ(y) ∣∣∣∣ ≤ C ρ σ3 √ n , where σ and ρ are respectively the variance and the absolute third moment of the parent distribution, Φ(·) is the unit normal cumulative distribution function, and C is an absolute constant. In thi...
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Let λ be a partition of n chosen from the Plancherel measure of the symmetric group Sn, let χλ(12) be the irreducible character of the symmetric group parameterized by λ evaluated on the transposition (12), and let dim(λ) be the dimension of the irreducible representation parameterized by λ. Fulman recently obtained the convergence rate of O(n−s) for any 0 < s < 1 2 in the central limit theorem...
متن کاملBerry-Esseen for Free Random Variables
An analogue of the Berry-Esseen inequality is proved for the speed of convergence of free additive convolutions of bounded probability measures. The obtained rate of convergence is of the order n, the same as in the classical case. An example with binomial measures shows that this estimate cannot be improved without imposing further restrictions on convolved measures. Courant Institute of Mathe...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1988
ISSN: 0386-2194
DOI: 10.3792/pjaa.64.381