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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 7 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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\paper Difference Operators and Determinantal Point Processes
\jour Funktsional. Anal. i Prilozhen.
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\pages 83--97
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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
    7. A. M. Borodin, Aleksandr I. Bufetov, Aleksei I. Bufetov, A. M. Vershik, V. E. Gorin, A. I. Molev, V. F. Molchanov, R. S. Ismagilov, A. A. Kirillov, M. L. Nazarov, Yu. A. Neretin, N. I. Nessonov, A. Yu. Okounkov, L. A. Petrov, S. M. Khoroshkin, “Grigori Iosifovich Olshanski (on his 70th birthday)”, Russian Math. Surveys, 74:3 (2019), 555–577  mathnet  crossref  crossref  adsnasa  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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