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Geometry of Permutation Limits

Rahman, Mustazee; Virág, Bálint; Vizer, Máté

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Authors

Bálint Virág

Máté Vizer



Abstract

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.

Citation

Rahman, M., Virág, B., & Vizer, M. (2019). Geometry of Permutation Limits. Combinatorica, 39, 933-960. https://doi.org/10.1007/s00493-019-3817-6

Journal Article Type Article
Acceptance Date Oct 30, 2018
Online Publication Date Jul 9, 2019
Publication Date 2019-08
Deposit Date Sep 25, 2019
Publicly Available Date Oct 6, 2021
Journal Combinatorica
Print ISSN 0209-9683
Electronic ISSN 1439-6912
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 39
Pages 933-960
DOI https://doi.org/10.1007/s00493-019-3817-6

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