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Nonintersecting paths with a staircase initial condition
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-7598-4521
2012 (English)In: Electronic Journal of Probability, ISSN 1083-6489, E-ISSN 1083-6489, Vol. 17, 1-24 p.Article in journal (Refereed) Published
Abstract [en]

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 -> infinity. 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.

Place, publisher, year, edition, pages
2012. Vol. 17, 1-24 p.
Keyword [en]
Random non-intersecting paths, determinantal point processes, random tilings
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-102125DOI: 10.1214/EJP.v17-1902ISI: 000307363700001Scopus ID: 2-s2.0-84864839472OAI: oai:DiVA.org:kth-102125DiVA: diva2:551245
Funder
Knut and Alice Wallenberg Foundation, KAW 2010.0063
Note

QC 20120910

Available from: 2012-09-10 Created: 2012-09-10 Last updated: 2017-12-07Bibliographically approved

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Duits, Maurice

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  • nn-NB
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  • Other locale
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