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

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Funktsional'nyi Analiz i ego Prilozheniya, 2008, Volume 42, Issue 3, Pages 23–44
DOI: https://doi.org/10.4213/faa2910 (Mi faa2910)

This article is cited in 38 scientific papers (total in 38 papers)

Nonintersecting Paths and the Hahn Orthogonal Polynomial Ensemble

V. E. Gorin

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

Full-text PDF (294 kB) Citations (38)

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DOI: https://doi.org/10.4213/faa2910

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.

Received: 12.03.2007

English version:
Functional Analysis and Its Applications, 2008, Volume 42, Issue 3, Pages 180–197
DOI: https://doi.org/10.1007/s10688-008-0027-1

Bibliographic databases:

Document Type: Article

UDC: 519.14+519.21

Language: Russian

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

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Linking options:

https://www.mathnet.ru/eng/faa2910

https://doi.org/10.4213/faa2910

https://www.mathnet.ru/eng/faa/v42/i3/p23

This publication is cited in the following 38 articles:

Amol Aggarwal, Jiaoyang Huang, “Edge Statistics for Lozenge Tilings of Polygons, II: Airy Line Ensemble”, Forum of Mathematics, Pi, 13 (2025)
Jiaoyang Huang, “Edge statistics for lozenge tilings of polygons, I: concentration of height function on strip domains”, Probab. Theory Relat. Fields, 188:1-2 (2024), 337
Anton Nazarov, Olga Postnova, Travis Scrimshaw, “Skew Howe duality and limit shapes of Young diagrams”, Journal of London Math Soc, 109:1 (2024)
Svetlana Gavrilova, Leonid Petrov, “Tilted biorthogonal ensembles, Grothendieck random partitions, and determinantal tests”, Sel. Math. New Ser., 30:3 (2024)
Maurice Duits, Erik Duse, Wenkui Liu, “Lozenge tilings of a hexagon and q-Racah ensembles”, J. Phys. A: Math. Theor., 57:40 (2024), 405202
Mark Adler, Pierre van Moerbeke, “Double interlacing in random tiling models”, Journal of Mathematical Physics, 64:3 (2023)
Peter J. Forrester, Shi-Hao Li, Bo-Jian Shen, Guo-Fu Yu, “q-Pearson pair and moments in q-deformed ensembles”, Ramanujan J, 60:1 (2023), 195
Leonid Petrov, Mikhail Tikhonov, “Asymptotics of noncolliding q-exchangeable random walks”, J. Phys. A: Math. Theor., 56:36 (2023), 365203
Evgeni Dimitrov, Alisa Knizel, “Asymptotics of discrete β-corners processes via two-level discrete loop equations”, Prob. Math. Phys., 3:2 (2022), 247
Charlier Ch., “Doubly Periodic Lozenge Tilings of a Hexagon and Matrix Valued Orthogonal Polynomials”, Stud. Appl. Math., 146:1 (2021), 3–80
Christophe Charlier, “Matrix orthogonality in the plane versus scalar orthogonality in a Riemann surface”, Transactions of Mathematics and Its Applications, 5:2 (2021)
Charlier C., Duits M., Kuijlaars A.B.J., Lenells J., “A Periodic Hexagon Tiling Model and Non-Hermitian Orthogonal Polynomials”, Commun. Math. Phys., 378:1 (2020), 401–466
Aggarwal A., “Limit Shapes and Local Statistics For the Stochastic Six-Vertex Model”, Commun. Math. Phys., 376:1 (2020), 681–746
Guionnet A., Huang J., “Rigidity and Edge Universality of Discrete Beta-Ensembles”, Commun. Pure Appl. Math., 72:9 (2019), 1875–1982
Berggren T., Duits M., “Correlation Functions For Determinantal Processes Defined By Infinite Block Toeplitz Minors”, Adv. Math., 356 (2019), 106766
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
Dan Betea, “Elliptically Distributed Lozenge Tilings of a Hexagon”, SIGMA, 14 (2018), 032, 39 pp.
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
Maurice Duits, “On global fluctuations for non-colliding processes”, Ann. Probab., 46:3 (2018)
Corwin I., Nica M., “Intermediate disorder directed polymers and the multi-layer extension of the stochastic heat equation”, Electron. J. Probab., 22 (2017), 13

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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