Local probabilities for random permutations without long cycles (Q276211)
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scientific article; zbMATH DE number 6576604
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Local probabilities for random permutations without long cycles |
scientific article; zbMATH DE number 6576604 |
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Local probabilities for random permutations without long cycles (English)
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3 May 2016
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Summary: We explore the probability \(\nu(n,r)\) that a permutation sampled from the symmetric group of order \(n!\) uniformly at random has no cycles of length exceeding \(r\), where \(1\leqslant r\leqslant n\) and \(n\to\infty\). Asymptotic formulas valid in specified regions for the ratio \(n/r\) are obtained using the saddle-point method combined with ideas originated in analytic number theory.
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symmetric group
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cycle structure
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short cycles
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saddle-point method
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