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Moscow Mathematical Journal, 2009, Volume 9, Number 4, Pages 749–774
DOI: https://doi.org/10.17323/1609-4514-2009-9-4-749-774
(Mi mmj363)
 

This article is cited in 19 scientific papers (total in 19 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
Full-text PDF Citations (19)
References:
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
Bibliographic databases:
Document Type: Article
MSC: Primary 15A52; Secondary 60G57
Language: English
Citation: Peter J. Forrester, Eric Nordenstam, “The anti-symmetric GUE minor process”, Mosc. Math. J., 9:4 (2009), 749–774
Citation in format AMSBIB
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\paper The anti-symmetric GUE minor process
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\yr 2009
\vol 9
\issue 4
\pages 749--774
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  • https://www.mathnet.ru/eng/mmj363
  • https://www.mathnet.ru/eng/mmj/v9/i4/p749
  • This publication is cited in the following 19 articles:
    1. Sung-Soo Byun, Leslie Molag, Nick Simm, “Large deviations and fluctuations of real eigenvalues of elliptic random matrices”, Electron. J. Probab., 30:none (2025)  crossref
    2. Anton Nazarov, Olga Postnova, Travis Scrimshaw, “Skew Howe duality and limit shapes of Young diagrams”, Journal of London Math Soc, 109:1 (2024)  crossref
    3. Vadim Gorin, Jiaming Xu, “Random sorting networks: Edge limit”, Ann. Inst. H. Poincaré Probab. Statist., 60:2 (2024)  crossref
    4. Forrester P.J., Ipsen J.R., Liu D.-Zh., Zhang L., “Orthogonal and Symplectic Harish-Chandra Integrals and Matrix Product Ensembles”, Random Matrices-Theor. Appl., 8:4 (2019), 1950015  crossref  mathscinet  zmath  isi  scopus
    5. Grabsch A., Cheipesh Y., Beenakker C.W.J., “Pfaffian Formula For Fermion Parity Fluctuations in a Superconductor and Application to Majorana Fusion Detection”, Ann. Phys.-Berlin, 531:10 (2019), 1900129  crossref  mathscinet  isi  scopus
    6. Gorin V. Rahman M., “Random Sorting Networks: Local Statistics Via Random Matrix Laws”, Probab. Theory Relat. Field, 175:1-2 (2019), 45–96  crossref  mathscinet  zmath  isi  scopus
    7. Dumitriu I. Paquette E., “Spectra of Overlapping Wishart Matrices and the Gaussian Free Field”, Random Matrices-Theor. Appl., 7:2 (2018), 1850003  crossref  mathscinet  zmath  isi  scopus
    8. Kargin V., “Limit Theorems For Linear Eigenvalue Statistics of Overlapping Matrices”, Electron. J. Probab., 20 (2015), 121, 1–30  crossref  mathscinet  isi  scopus
    9. Gorin V., Panova G., “Asymptotics of Symmetric Polynomials With Applications To Statistical Mechanics and Representation Theory”, Ann. Probab., 43:6 (2015), 3052–3132  crossref  mathscinet  zmath  isi  elib  scopus
    10. Panova G., “Lozenge Tilings With Free Boundaries”, Lett. Math. Phys., 105:11 (2015), 1551–1586  crossref  mathscinet  zmath  isi  scopus
    11. Ferrari P.L., Frings R., “Perturbed Gue Minor Process and Warren's Process with Drifts”, J. Stat. Phys., 154:1-2 (2014), 356–377  crossref  mathscinet  zmath  isi  elib  scopus
    12. Borodin A., Ferrari P.L., “Anisotropic Growth of Random Surfaces in 2+1 Dimensions”, Commun. Math. Phys., 325:2 (2014), 603–684  crossref  mathscinet  zmath  isi  elib  scopus
    13. Petrov L., “Asymptotics of Random Lozenge Tilings Via Gelfand-Tsetlin Schemes”, Probab. Theory Relat. Field, 160:3-4 (2014), 429–487  crossref  mathscinet  zmath  isi  elib  scopus
    14. Adler M., Nordenstam E., Van Moerbeke P., “the Dyson Brownian Minor Process”, Ann. Inst. Fourier, 64:3 (2014), 971–1009  crossref  mathscinet  zmath  isi
    15. Fleming B.J., Forrester P.J., Nordenstam E., “A finitization of the bead process”, Probab Theory Related Fields, 152:1–2 (2012), 321–356  crossref  mathscinet  zmath  isi  elib  scopus
    16. Fleming B.J., Forrester P.J., “Interlaced particle systems and tilings of the Aztec diamond”, J. Stat. Phys., 142:3 (2011), 441–459  crossref  mathscinet  zmath  adsnasa  isi  scopus
    17. Ferrari P.L., Frings R., “On the partial connection between random matrices and interacting particle systems”, J. Stat. Phys., 141:4 (2010), 613–637  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    18. Dumitriu I., Forrester P.J., “Tridiagonal realization of the antisymmetric Gaussian $\beta$-ensemble”, J. Math. Phys., 51:9 (2010), 093302, 25 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    19. Alexei Borodin, Patrik L. Ferrari, Tomohiro Sasamoto, “Two Speed TASEP”, J Stat Phys, 137:5-6 (2009), 936  crossref
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