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• W3100223658 abstract "A sorting network is a shortest path from $12 cdots n$ to $n cdots 2 1$ 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 $pi$-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 $epsilon$ of the edge are within $sqrt{2epsilon}$ of a sine curve in uniform norm." @default.
• W3100223658 created "2020-11-23" @default.
• W3100223658 creator A5075377725 @default.
• W3100223658 creator A5082860022 @default.
• W3100223658 date "2019-11-15" @default.
• W3100223658 modified "2023-09-26" @default.
• W3100223658 title "Circular support in random sorting networks" @default.
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• W3100223658 doi "https://doi.org/10.1090/tran/7819" @default.
• W3100223658 hasPublicationYear "2019" @default.
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