The Berry–Esseen Bound in the Theory of Random Permutations |
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| Authors: | Manstavičius E. |
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| Affiliation: | (1) Department of Mathematics, Vilnius University, Naugarduko str. 24, LT-2600 Vilnius, Lithuania E-mail |
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| Abstract: | The convergence rate in the central limit theorem for linear combinations of the cycle lengths of a random permutation is examined. It is shown that, in contrast to the Berry-Esseen theorem, the optimal estimate in terms of the sum of the third absolute moments has the exponent 2/3. |
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| Keywords: | random permutation Berry-Esseen theorem Central limit remainder term random mappings symmetric group |
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