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A pattern theorem for random sorting networks

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	A pattern theorem for random sorting networks
2.	Creator	Author's name, affiliation, country	Omer Angel; University of British Columbia; Canada
2.	Creator	Author's name, affiliation, country	Vadim Gorin; Massachusetts Institute of Technology and Institute for Information Transmission Problems of Moscow; United States
2.	Creator	Author's name, affiliation, country	Alexander E Holroyd; Microsoft Research Redmond; United States
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Sorting network; random sorting; reduced word; pattern; Young tableau
3.	Subject	Subject classification	60C05; 05E10; 68P10
4.	Description	Abstract	A sorting network is a shortest path from $12\cdots n$ to $n\cdots 21$ 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 $n\to\infty$. 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  $0$.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	University of Toronto; NSERC; Sloan Foundation; Microsoft Research; Moebius Foundation; Dynasty' foundation; RFBR
7.	Date	(YYYY-MM-DD)	2012-11-19
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/2448
10.	Identifier	Digital Object Identifier	10.1214/EJP.v17-2448
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 17
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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