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 \(n \rightarrow \infty \).
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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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Jin, K. The Limit of the Empirical Measure of the Product of Two Independent Mallows Permutations. J Theor Probab 32, 1688–1728 (2019). https://doi.org/10.1007/s10959-019-00917-w
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DOI: https://doi.org/10.1007/s10959-019-00917-w