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Generating a Random Signed Permutation with Random Reversals

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Signed permutations form a group known as the hyperoctahedral group. We bound the rate of convergence to uniformity for a certain random walk on the hyperoctahedral group that is generated by random reversals. Specifically, we determine that O(n log n) steps are both necessary and sufficient for total variation distance and ℓ2 distance to become small. This random walk arose as the result of an effort in molecular biology to model certain types of genome rearrangements.

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References

  1. V. Bafna P. Pevzner (1996) ArticleTitleGenome rearrangements and sorting by reversals SIAM J. Comput. 25 272–289 Occurrence Handle10.1137/S0097539793250627

    Article  Google Scholar 

  2. P. Diaconis (1988) Group Representations in Probability and Statistics Institute of Mathematical Statistics Hayward, CA

    Google Scholar 

  3. P. Diaconis L. Saloff-Coste (1993) ArticleTitleComparison techniques for random walk on finite groups Ann. Probab. 21 2131–2156

    Google Scholar 

  4. P. Diaconis M. Shahshahani (1981) ArticleTitleGenerating a random permutation with random transpositions Z. Wahrsch. Verw. Gebiete 57 159–179 Occurrence Handle10.1007/BF00535487

    Article  Google Scholar 

  5. R. Durrett (2003) ArticleTitleShuffling chromosomes J. Theoret. Prob. 16 725–750 Occurrence Handle10.1023/A:1025676617383

    Article  Google Scholar 

  6. S. Hannenhalli P. Pevzner (1999) ArticleTitleTransforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals J. Assoc. Comput. Mach. 46 1–27

    Google Scholar 

  7. G. James A. Kerber (1981) The Representation Theory of the Symmetric Group. Encyclopedia of Mathematics and its Applications, Vol. 16 Addison–Wesley Reading, MA

    Google Scholar 

  8. H. Kaplan R. Shamir Tarjan R. (2000) ArticleTitleA faster and simpler algorithm for sorting signed permutations by reversals SIAM J. Comput. 29 880–892 Occurrence Handle10.1137/S0097539798334207

    Article  Google Scholar 

  9. C. H. Schoolfield (2002) ArticleTitleRandom walks on wreath products of groups J. Theoret. Prob. 15 667–693 Occurrence Handle10.1023/A:1016219932004

    Article  Google Scholar 

  10. J.-P. Serre (1977) Linear Representations of Finite Groups. Graduate Texts in Mathematics NumberInSeriesVol. 42 Springer-Verlag New York

    Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Statistics, The University of Florida, Gainesville, FL, 32611, USA

    Clyde H. Schoolfield Jr.

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  1. Clyde H. Schoolfield Jr.
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Correspondence to Clyde H. Schoolfield Jr..

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Schoolfield, C.H. Generating a Random Signed Permutation with Random Reversals. J Theor Probab 18, 911–931 (2005). https://doi.org/10.1007/s10959-005-7532-4

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  • DOI: https://doi.org/10.1007/s10959-005-7532-4

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