Geometry of Permutation Limits
Probability
2019-11-05 v4 Combinatorics
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.
Keywords
Cite
@article{arxiv.1609.03891,
title = {Geometry of Permutation Limits},
author = {Mustazee Rahman and Balint Virag and Mate Vizer},
journal= {arXiv preprint arXiv:1609.03891},
year = {2019}
}
Comments
Final version; to appear in Combinatorica