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- W2110562284 abstract "A sorting network is a shortest path from $12cdots n$ to $ncdots 21$ in the Cayley graph of the symmetric group $S_n$ generated by nearest-neighbor swaps. A pattern is a sequence of swaps that forms an initial segment of some sorting network. We prove that in a uniformly random $n$-element sorting network, any fixed pattern occurs in at least $c n^2$ disjoint space-time locations, with probability tending to $1$ exponentially fast as $ntoinfty$. Here $c$ is a positive constant which depends on the choice of pattern. As a consequence, the probability that the uniformly random sorting network is geometrically realizable tends to $0$." @default.
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- W2110562284 date "2012-01-01" @default.
- W2110562284 modified "2023-09-26" @default.
- W2110562284 title "A pattern theorem for random sorting networks" @default.
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- W2110562284 doi "https://doi.org/10.1214/ejp.v17-2448" @default.
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