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Determinantal measures related to big q-Jacobi polynomials

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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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Authors and Affiliations

  1. Department of Mathematics, MIT, Cambridge, USA

    V. E. Gorin

  2. Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    V. E. Gorin

  3. Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    G. I. Olshanski

Authors
  1. V. E. Gorin
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  2. G. I. Olshanski
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Corresponding author

Correspondence to V. E. Gorin.

Additional information

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

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