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Local probabilities and total variation distance for random permutations

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Abstract

We are concerned with permutations taken uniformly at random from the symmetric group. Firstly, we study the probability of a permutation missing short cycles. Secondly, the result is employed to establish a formula for total variation distance between the process of multiplicities of cycle lengths in a random permutation and a process of independent Poisson random variables. We apply an analytic approach originated in number theory (K. Gyory et al. (Eds.) in Number Theory in Progress, 1999).

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Authors and Affiliations

  1. Vilnius University, Vilnius, LT-03225, Lithuania

    Eugenijus Manstavičius & Robertas Petuchovas

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  1. Eugenijus Manstavičius
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  2. Robertas Petuchovas
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Correspondence to Robertas Petuchovas.

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Manstavičius, E., Petuchovas, R. Local probabilities and total variation distance for random permutations. Ramanujan J 43, 679–696 (2017). https://doi.org/10.1007/s11139-016-9786-0

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  • DOI: https://doi.org/10.1007/s11139-016-9786-0

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