Nonintersecting paths with a staircase initial condition
- Creators
- Breuer, Jonathan
- Duits, Maurice
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 → ∞. 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.
Additional Information
This work is licensed under a Creative Commons Attribution 3.0 License. Submitted to EJP on March 24, 2012, final version accepted on July 13, 2012. Publication Date: August 3, 2012. Supported by grants KAW 2010.0063 (Knut and Alice Wallenberg Fnd.) and 1105/10 (Israel Science Fnd.)Attached Files
Published - 1902-10780-1-PB.pdf
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Additional details
- Eprint ID
- 33932
- Resolver ID
- CaltechAUTHORS:20120907-110621501
- 2010.0063
- Knut and Alice Wallenberg Fnd.
- 1105/10
- Israel Science Fnd.
- Created
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2012-09-07Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field