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Funktsional. Anal. i Prilozhen., 2008, Volume 42, Issue 3, Pages 23–44 (Mi faa2910)  

This article is cited in 23 scientific papers (total in 23 papers)

Nonintersecting Paths and the Hahn Orthogonal Polynomial Ensemble

V. E. Gorin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We compute the bulk limit of the correlation functions for the uniform measure on lozenge tilings of a hexagon. The limiting determinantal process is a translation-invariant extension of the discrete sine process, which can also be described by an ergodic Gibbs measure with appropriate parameters.

Keywords: tiling of a hexagon, plane partition, determinantal process, orthogonal polynomial ensemble


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English version:
Functional Analysis and Its Applications, 2008, 42:3, 180–197

Bibliographic databases:

UDC: 519.14+519.21
Received: 12.03.2007

Citation: V. E. Gorin, “Nonintersecting Paths and the Hahn Orthogonal Polynomial Ensemble”, Funktsional. Anal. i Prilozhen., 42:3 (2008), 23–44; Funct. Anal. Appl., 42:3 (2008), 180–197

Citation in format AMSBIB
\by V.~E.~Gorin
\paper Nonintersecting Paths and the Hahn Orthogonal Polynomial Ensemble
\jour Funktsional. Anal. i Prilozhen.
\yr 2008
\vol 42
\issue 3
\pages 23--44
\jour Funct. Anal. Appl.
\yr 2008
\vol 42
\issue 3
\pages 180--197

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    This publication is cited in the following articles:
    1. G. I. Olshanskii, “Difference Operators and Determinantal Point Processes”, Funct. Anal. Appl., 42:4 (2008), 317–329  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. V. E. Gorin, “Non-colliding Jacobi processes as limits of Markov chains on the Gelfand–Tsetlin graph”, J. Math. Sci. (N. Y.), 158:6 (2009), 819–837  mathnet  crossref  zmath  elib  elib
    3. Borodin A., Gorin V., “Shuffling algorithm for boxed plane partitions”, Adv. Math., 220:6 (2009), 1739–1770  crossref  mathscinet  zmath  isi  elib
    4. Borodin A., Gorin V., Rains E.M., “$q$-Distributions on boxed plane partitions”, Selecta Math (N.S.), 16:4 (2010), 731–789  crossref  mathscinet  zmath  isi
    5. Grünbaum F.A., “An urn model associated with Jacobi polynomials”, Commun. Appl. Math. Comput. Sci., 5:1 (2010), 55–63  crossref  mathscinet  zmath  isi
    6. Forrester P.J., Nagao T., “Determinantal correlations for classical projection processes”, J. Stat. Mech., 2011, P08011, 28 pp.  crossref  isi
    7. Jafarov E.I., Stoilova N.I., Van der Jeugt J., “The $\mathfrak{su}(2)_\alpha$ Hahn oscillator and a discrete Fourier-Hahn transform”, J. Phys. A, 44:35 (2011), 355205, 18 pp.  crossref  zmath  isi  elib
    8. Boutillier C., Mkrtchyan S., Reshetikhin N., Tingley P., “Random skew plane partitions with a piecewise periodic back wall”, Ann. Henri Poincaré, 13:2 (2012), 271–296  crossref  mathscinet  zmath  adsnasa  isi
    9. Fleming B.J., Forrester P.J., Nordenstam E., “A finitization of the bead process”, Probab. Theory Relat. Fields, 152:1-2 (2012), 321–356  crossref  mathscinet  zmath  isi
    10. Borodin A., Gorin V., “Markov Processes of Infinitely Many Nonintersecting Random Walks”, Probab. Theory Relat. Field, 155:3-4 (2013), 935–997  crossref  mathscinet  zmath  isi
    11. 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
    12. Mkrtchyan S., “Plane Partitions With Two-Periodic Weights”, Lett. Math. Phys., 104:9 (2014), 1053–1078  crossref  mathscinet  zmath  adsnasa  isi
    13. Petrov L., “Asymptotics of Uniformly Random Lozenge Tilings of Polygons. Gaussian Free Field”, Ann. Probab., 43:1 (2015), 1–43  crossref  mathscinet  zmath  isi
    14. Bufetov A., Gorin V., “Representations of Classical Lie Groups and Quantized Free Convolution”, Geom. Funct. Anal., 25:3 (2015), 763–814  crossref  mathscinet  zmath  isi  elib
    15. Knizel A., “Moduli Spaces of q -Connections and Gap Probabilities”, Int. Math. Res. Notices, 2016, no. 22, 6921–6954  crossref  mathscinet  isi
    16. Corwin I., Nica M., “Intermediate disorder directed polymers and the multi-layer extension of the stochastic heat equation”, Electron. J. Probab., 22 (2017), 13  crossref  mathscinet  zmath  isi  scopus
    17. Gorin V., “Bulk Universality For Random Lozenge Tilings Near Straight Boundaries and For Tensor Products”, Commun. Math. Phys., 354:1 (2017), 317–344  crossref  mathscinet  zmath  isi
    18. Borodin A., Olshanski G., “The Asep and Determinantal Point Processes”, Commun. Math. Phys., 353:2 (2017), 853–903  crossref  mathscinet  zmath  isi
    19. Borodin A., Gorin V., Guionnet A., “Gaussian Asymptotics of Discrete Beta-Ensembles”, Publ. Math. IHES, 2017, no. 125, 1–78  crossref  mathscinet  zmath  isi
    20. Adler M., Johansson K., van Moerbeke P., “Lozenge Tilings of Hexagons With Cuts and Asymptotic Fluctuations: a New Universality Class”, Math. Phys. Anal. Geom., 21:1 (2018), 9  crossref  mathscinet  isi
    21. Dan Betea, “Elliptically Distributed Lozenge Tilings of a Hexagon”, SIGMA, 14 (2018), 032, 39 pp.  mathnet  crossref
    22. Adler M., Johansson K., van Moerbeke P., “Tilings of Non-Convex Polygons, Skew-Young Tableaux and Determinantal Processes”, Commun. Math. Phys., 364:1 (2018), 287–342  crossref  mathscinet  zmath  isi  scopus
    23. Guionnet A., Huang J., “Rigidity and Edge Universality of Discrete Beta-Ensembles”, Commun. Pure Appl. Math., 72:9 (2019), 1875–1982  crossref  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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