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Geometry of Permutation Limits

Rahman, Mustazee and Virág, Bálint and Vizer, Máté (2019) 'Geometry of Permutation Limits.', Combinatorica., 39 . pp. 933-960.


This paper initiates a limit theory of permutation valued processes, building on the recent theory of permutons. We apply this to study the asymptotic behaviour of random sorting networks. We prove that the Archimedean path, the conjectured limit of random sorting networks, is the unique path from the identity to the reverse permuton having minimal energy in an appropriate metric. Together with a recent large deviations result (Kotowski, 2016), it implies the Archimedean limit for the model of relaxed random sorting networks.

Item Type:Article
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Publisher statement:This is a post-peer-review, pre-copyedit version of a journal article published in Combinatorica. The final authenticated version is available online at:
Date accepted:30 October 2018
Date deposited:06 October 2021
Date of first online publication:09 July 2019
Date first made open access:06 October 2021

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