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2012 Nonintersecting paths with a staircase initial condition
Jonathan Breuer, Maurice Duits
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Electron. J. Probab. 17: 1-24 (2012). DOI: 10.1214/EJP.v17-1902


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.


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Jonathan Breuer. Maurice Duits. "Nonintersecting paths with a staircase initial condition." Electron. J. Probab. 17 1 - 24, 2012.


Accepted: 3 August 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1266.60089
MathSciNet: MR2959066
Digital Object Identifier: 10.1214/EJP.v17-1902

Primary: 60G55

Keywords: Determinantal point processes , Random non-intersecting paths , random tilings


Vol.17 • 2012
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