Two new proofs of the Erdös–Kac Theorem, with bound on the rate of convergence, by Stein's method for distributional approximations
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Publication:3636900
DOI10.1017/S0305004109002412zbMath1195.11100OpenAlexW2110115601MaRDI QIDQ3636900
Publication date: 30 June 2009
Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1017/s0305004109002412
Related Items (15)
Mod-\(\phi\) convergence: approximation of discrete measures and harmonic analysis on the torus ⋮ The Berry-Esseen bound for identically distributed random variables by Stein method ⋮ A weighted version of the Erdős-Kac theorem ⋮ On the counting function of semiprimes ⋮ Gaps between prime divisors and analogues in Diophantine geometry ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Mod-discrete expansions ⋮ Inequalities for integrals of modified Bessel functions and expressions involving them ⋮ Large and moderate deviation principles for the Erdős-Kac theorem in function fields ⋮ Bounds for an integral of the modified Bessel function of the first kind and expressions involving it ⋮ Unnamed Item ⋮ An algebra of Stein operators ⋮ Hardy, Littlewood and probability ⋮ New error bounds in multivariate normal approximations via exchangeable pairs with applications to Wishart matrices and fourth moment theorems
Cites Work
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- On coupling constructions and rates in the CLT for dependent summands with applications to the antivoter model and weighted \(U\)-statistics
- On the Central Limit Theorem for the Prime Divisor Function
- Probabilistic methods in the theory of numbers
- Note on the Number of Prime Divisors of Integers
- On the Gaussian Law of Errors in the Theory of Additive Functions
- The Gaussian Law of Errors in the Theory of Additive Number Theoretic Functions
- On the Size of Certain Number-Theoretic Functions
- Normal approximations by Stein's method
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