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Central limit theorem for the prefix exchange distance under Ewens sampling formula

Authors
  • Grusea, Simona
  • Labarre, Anthony
Publication Date
Feb 28, 2020
Source
Kaleidoscope Open Archive
Keywords
Language
English
License
Unknown
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Abstract

The prefix exchange distance of a permutation is the length of its shortest factorisation into transpositions that all contain 1. Using a probabilistic approach, we obtain expressions for the mean and the variance, and prove the asymptotic normality of the distribution of this distance for a random permutation verifying the Ewens sampling formula. Analogous results in the uniform setting follow as simple corollaries.

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