Geodesic
Determinantal Measures Related to Big $q$-Jacobi Polynomials
Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 3, pp. 70-74

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We define a novel combinatorial object—the extended Gelfand–Tsetlin graph with cotransition probabilities depending on a parameter $q$. The boundary of this graph admits an explicit description. We introduce a family of probability measures on the boundary and describe their correlation functions. These measures are a $q$-analogue of the spectral measures studied earlier in the context of the problem of harmonic analysis on the infinite-dimensional unitary group.
Keywords: Gelfand–Tsetlin graph, determinantal measures, big $q$-Jacobi polynomials, basic hypergeometric series. 
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     author = {V. Gorin and G. I. Olshanskii},
     title = {Determinantal {Measures} {Related} to {Big} $q${-Jacobi} {Polynomials}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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V. Gorin; G. I. Olshanskii. Determinantal Measures Related to Big $q$-Jacobi Polynomials. Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 3, pp. 70-74. http://geodesic.mathdoc.fr/item/FAA_2015_49_3_a6/