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Nonintersecting paths with a staircase initial condition

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1.	Title	Title of document	Nonintersecting paths with a staircase initial condition
2.	Creator	Author's name, affiliation, country	Jonathan Breuer; The Hebrew University of Jerusalem; Israel
2.	Creator	Author's name, affiliation, country	Maurice Duits; Royal Institute of Technology; Sweden
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Random non-intersecting paths, Determinantal point processes, random tilings
3.	Subject	Subject classification	60G55
4.	Description	Abstract	We consider an ensemble of $N$ discrete nonintersecting paths starting from equidistant points and ending at consecutive integers. Our first result is an explicit formula for the correlation kernel that allows us to analyze the process as $N\to \infty$.   In that limit we obtain a new general class of kernels describing the local correlations close to the equidistant starting points. As the distance between the starting points goes to infinity, the correlation kernel converges to that of a single random walker. As the distance to the starting line increases, however, the local correlations converge to the sine kernel. Thus, this class interpolates between the sine kernel and an ensemble of independent particles. We also compute the scaled simultaneous limit, with both the distance between particles and the distance to the starting line going to infinity, and obtain a process with number variance saturation, previously studied by Johansson.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2012-08-03
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/1902
10.	Identifier	Digital Object Identifier	10.1214/EJP.v17-1902
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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