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This article is cited in 18 scientific papers (total in 18 papers)
The anti-symmetric GUE minor process
Peter J. Forrestera, Eric Nordenstamb a University of Melbourne, Department of Mathematics and Statistics
b Institutionen för Matematik, Swedish Royal Institute of Technology (KTH), Stockholm, Sweden
Abstract:
Our study is initiated by a multi-component particle system underlying the tiling of a half hexagon by three species of rhombi. In this particle system species $j$ consists of $\lfloor j/2\rfloor$ particles which are interlaced with neigbouring species. The joint probability density function (PDF) for this particle system is obtained, and is shown in a suitable scaling limit to coincide with the joint eigenvalue PDF for the process formed by the successive minors of anti-symmetric GUE matrices, which in turn we compute from first principles. The correlations for this process are determinantal and we give an explicit formula for the corresponding correlation kernel in terms of Hermite polynomials. Scaling limits of the latter are computed, giving rise to the Airy kernel, extended Airy kernel and bead kernel at the soft edge and in the bulk, as well as a new kernel at the hard edge.
Key words and phrases:
random matrices, tilings, point processes.
Received: April 27, 2008
Citation:
Peter J. Forrester, Eric Nordenstam, “The anti-symmetric GUE minor process”, Mosc. Math. J., 9:4 (2009), 749–774
Linking options:
https://www.mathnet.ru/eng/mmj363 https://www.mathnet.ru/eng/mmj/v9/i4/p749
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Abstract page: | 229 | References: | 66 |
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