Dr Mustazee Rahman mustazee.rahman@durham.ac.uk
Associate Professor
Geometry of Permutation Limits
Rahman, Mustazee; Virág, Bálint; Vizer, Máté
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 | Mar 28, 2024 |
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 |
Files
Accepted Journal Article
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Copyright 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: https://doi.org/10.1007/s00493-019-3817-6
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