Abstract
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.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 49, No. 3, pp. 70–74, 2015
Original Russian Text Copyright © by V. E. Gorin and G. I. Olshanski
The research of G. I. Olshanski was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences at the expense of the Russian Science Foundation (project no. 14-50-00150).
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Gorin, V.E., Olshanski, G.I. Determinantal measures related to big q-Jacobi polynomials. Funct Anal Its Appl 49, 214–217 (2015). https://doi.org/10.1007/s10688-015-0107-y
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DOI: https://doi.org/10.1007/s10688-015-0107-y