### Abstract

A sorting network is a shortest path from 12···n to n···21 in the Cayley graph of the symmetric group generated by adjacent transpositions. For a uniform random sorting network, we prove that in the global limit, particle trajectories are supported on π-Lipschitz paths. We show that the weak limit of the permutation matrix of a random sorting network at any fixed time is supported within a particular ellipse. This is conjectured to be an optimal bound on the support. We also show that in the global limit, trajectories of particles that start within distance #x220A; of the edge are within √2#x220A; of a sine curve in uniform norm.

Original language | English (US) |
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Pages (from-to) | 1529-1553 |

Number of pages | 25 |

Journal | Transactions of the American Mathematical Society |

Volume | 373 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2020 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

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## Cite this

Dauvergne, D., & Virág, B. (2020). Circular support in random sorting networks.

*Transactions of the American Mathematical Society*,*373*(3), 1529-1553. https://doi.org/10.1090/tran/7819