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

Ke Jin ()
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Ke Jin: University of Delaware

Journal of Theoretical Probability, 2019, vol. 32, issue 4, 1688-1728

Abstract: Abstract The Mallows measure is a probability measure on $$S_n$$ S n where the probability of a permutation $$\pi $$ π is proportional to $$q^{l(\pi )}$$ q l ( π ) with $$q > 0$$ q > 0 being a parameter and $$l(\pi )$$ l ( π ) the number of inversions in $$\pi $$ π . 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 $$n(1-q)$$ n ( 1 - q ) has limit in $$\mathbb {R}$$ R as $$n \rightarrow \infty $$ n → ∞ .

Keywords: Mallows measure; Random permutation; Convergence of measure; 60F05; 60B15; 05A05 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10959-019-00917-w

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