The number of cycles in random permutations without long cycles is\n asymptotically Gaussian

2016/05/26 by Volker Betz, Betz, Volker, Helge Schäfer +1
Computer Science · Decision Sciences · Mathematics · #60C05 #60F05 #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Statistical Distribution Estimation and Applications

paper · pdf · doi:10.48550/arxiv.1605.08383

openalex publication_date 2016/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For uniform random permutations conditioned to have no long cycles, we prove\nthat the total number of cycles satisfies a central limit theorem. Under\nadditional assumptions on the asymptotic behavior of the set of allowed cycle\nlengths, we derive asymptotic expansions for the corresponding expected value\nand variance.\n

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