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01921 am a22003133u 4500 |
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89523 |
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|a dc
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|a Angel, Omer
|e author
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|a Massachusetts Institute of Technology. Department of Mathematics
|e contributor
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|a Gorin, Vadim
|e contributor
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|a Gorin, Vadim
|e author
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|a Holroyd, Alexander E
|e author
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|a A pattern theorem for random sorting networks
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|b Institute of Mathematical Statistics,
|c 2014-09-15T14:57:23Z.
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|z Get fulltext
|u http://hdl.handle.net/1721.1/89523
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|a A sorting network is a shortest path from 12⋯n to n⋯21 in the Cayley graph of the symmetric group S[subscript 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 cn[superscript 2] disjoint space-time locations, with probability tending to 1 exponentially fast as n→∞. 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.
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|a University of Toronto
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|a Natural Sciences and Engineering Research Council of Canada
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|a Alfred P. Sloan Foundation
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|a Microsoft Research
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|a Möbius Contest Foundation for Young Scientists
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|a Dynasty Foundation
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|a Russian Foundation for Basic Research (RFBR-CNRS grant 10-01-93114)
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|a Murmansk State Humanities University ("Development of the scientific potential of the higher school")
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|a Simons Foundation (IUM-Simons Foundation scholarship)
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|a Independent University of Moscow (IUM-Simons Foundation scholarship)
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|a en_US
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|a Article
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|t Electronic Journal of Probability
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