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Probl. Peredachi Inf., 2011, Volume 47, Issue 3, Pages 39–58 (Mi ppi2053)  

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

Large Systems

On a sequence of random distance graphs subject to the zero-one law

M. E. Zhukovskii

Probability Theory Chair, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University

Abstract: It is known that an Erdős–Rényi random graph obeys a zero-one law for first-order properties. The study of these laws started in 1969 with the work of Yu. V. Glebskii, D. I. Kogan, M. I. Liogon'kii, and V. A. Talanov. We proved in our previous works that a random distance graph does not obey the zero-one law. In this paper a sequence of random distance graphs obeying the zero-one law is obtained.

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English version:
Problems of Information Transmission, 2011, 47:3, 251–268

Bibliographic databases:

UDC: 621.391.1+519.1
Received: 07.12.2010
Revised: 10.05.2011

Citation: M. E. Zhukovskii, “On a sequence of random distance graphs subject to the zero-one law”, Probl. Peredachi Inf., 47:3 (2011), 39–58; Problems Inform. Transmission, 47:3 (2011), 251–268

Citation in format AMSBIB
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\by M.~E.~Zhukovskii
\paper On a~sequence of random distance graphs subject to the zero-one law
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\yr 2011
\vol 47
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\pages 39--58
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\transl
\jour Problems Inform. Transmission
\yr 2011
\vol 47
\issue 3
\pages 251--268
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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. S. N. Popova, “Zero-one law for random distance graphs with vertices in $\{-1,0,1\}^n$”, Problems Inform. Transmission, 50:1 (2014), 57–78  mathnet  crossref  isi
    2. Popova S.N., “Zero-One Laws For Random Distance Graphs With Vertices in (0,1)(N)”, Dokl. Math., 90:2 (2014), 535–538  crossref  mathscinet  zmath  isi  elib  scopus
    3. M. E. Zhukovskii, A. M. Raigorodskii, “Random graphs: models and asymptotic characteristics”, Russian Math. Surveys, 70:1 (2015), 33–81  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. S. N. Popova, “Zero-one law for random subgraphs of some distance graphs with vertices in $\mathbb Z^n$”, Sb. Math., 207:3 (2016), 458–478  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    5. S. N. Popova, “Zero-one laws for random graphs with vertices in a Boolean cube”, Siberian Adv. Math., 27:1 (2017), 26–75  mathnet  crossref  crossref  mathscinet  elib
    6. A. V. Burkin, M. E. Zhukovskii, “Small subgraphs and their extensions in a random distance graph”, Sb. Math., 209:2 (2018), 163–186  mathnet  crossref  crossref  adsnasa  isi  elib
  • Проблемы передачи информации Problems of Information Transmission
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