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Journal of Theoretical Probability

, Volume 32, Issue 4, pp 1688–1728 | Cite as

The Limit of the Empirical Measure of the Product of Two Independent Mallows Permutations

Article
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Abstract

The Mallows measure is a probability measure on \(S_n\) where the probability of a permutation \(\pi \) is proportional to \(q^{l(\pi )}\) with \(q > 0\) being a parameter and \(l(\pi )\) the number of inversions in \(\pi \). We show the convergence of the random empirical measure of the product of two independent permutations drawn from the Mallows measure, when q is a function of n and \(n(1-q)\) has limit in \(\mathbb {R}\) as \(n \rightarrow \infty \).

Keywords

Mallows measure Random permutation Convergence of measure 

Mathematics Subject Classification (2010)

60F05 60B15 05A05 

Notes

Acknowledgements

I am grateful to my supervisor Nayantara Bhatnagar for her helpful advice and suggestions during the research as well as her guidance in the completion of this paper. I was supported in part by NSF grant DMS-1261010 and Sloan Research Fellowship.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of DelawareNewarkUSA

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