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Funktsional. Anal. i Prilozhen., 2008, Volume 42, Issue 4, Pages 83–97 (Mi faa2932)  

This article is cited in 6 scientific papers (total in 6 papers)

Difference Operators and Determinantal Point Processes

G. I. Olshanskii

Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: The paper deals with a family $\{P\}$ of determinantal point processes arising in representation theory and random matrix theory. The processes $P$ live on a one-dimensional lattice and have a number of special properties. One of them is that the correlation kernel $K(x,y)$ of each of the processes is a projection kernel: it determines a projection $K$ in the Hilbert $\ell^2$ space on the lattice. Moreover, the projection $K$ can be realized as the spectral projection onto the positive part of the spectrum of a self-adjoint difference second-order operator $D$. The aim of the paper is to show that the difference operators $D$ can be efficiently used in the study of limit transitions within the family $\{P\}$.

Keywords: point process, determinantal process, orthogonal polynomial ensemble, Plancherel measure, z-measure, Meixner polynomial, Krawtchouk polynomial

DOI: https://doi.org/10.4213/faa2932

Full text: PDF file (258 kB)
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English version:
Functional Analysis and Its Applications, 2008, 42:4, 317–329

Bibliographic databases:

UDC: 519.218.5
Received: 12.09.2008

Citation: G. I. Olshanskii, “Difference Operators and Determinantal Point Processes”, Funktsional. Anal. i Prilozhen., 42:4 (2008), 83–97; Funct. Anal. Appl., 42:4 (2008), 317–329

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    2. Olshanski G., “The quasi-invariance property for the Gamma kernel determinantal measure”, Adv. Math., 226:3 (2011), 2305–2350  crossref  mathscinet  zmath  isi  elib
    3. J. Math. Sci. (N. Y.), 190:3 (2013), 451–458  mathnet  crossref  mathscinet
    4. Mkrtchyan S., “Entropy of Schur-Weyl Measures”, Ann. Inst. Henri Poincare-Probab. Stat., 50:2 (2014), 678–713  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Knizel A., “Moduli Spaces of q -Connections and Gap Probabilities”, Int. Math. Res. Notices, 2016, no. 22, 6921–6954  crossref  mathscinet  isi
    6. Borodin A. Olshanski G., “The Asep and Determinantal Point Processes”, Commun. Math. Phys., 353:2 (2017), 853–903  crossref  mathscinet  zmath  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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