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Teor. Veroyatnost. i Primenen., 1970, Volume 15, Issue 3, Pages 469–497 (Mi tvp1856)  

This article is cited in 24 scientific papers (total in 24 papers)

Definition of random variables by conditional distributions

R. L. Dobrushin

Moscow

Abstract: The paper studies the question about the existence and uniqueness of random fields with a given system of conditional distributions.

Full text: PDF file (1697 kB)

English version:
Theory of Probability and its Applications, 1970, 15:3, 458–486

Bibliographic databases:

Received: 04.03.1969

Citation: R. L. Dobrushin, “Definition of random variables by conditional distributions”, Teor. Veroyatnost. i Primenen., 15:3 (1970), 469–497; Theory Probab. Appl., 15:3 (1970), 458–486

Citation in format AMSBIB
\Bibitem{Dob70}
\by R.~L.~Dobrushin
\paper Definition of random variables by conditional distributions
\jour Teor. Veroyatnost. i Primenen.
\yr 1970
\vol 15
\issue 3
\pages 469--497
\mathnet{http://mi.mathnet.ru/tvp1856}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=298716}
\zmath{https://zbmath.org/?q=an:0264.60037}
\transl
\jour Theory Probab. Appl.
\yr 1970
\vol 15
\issue 3
\pages 458--486
\crossref{https://doi.org/10.1137/1115049}


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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. R. L. Dobrushin, “Gibbsian random fields for particles without hard core”, Theoret. and Math. Phys., 4:1 (1970), 705–719  mathnet  crossref  mathscinet  zmath
    2. R. L. Dobrushin, “Asymptotic behavior of Gibbsian distributions for lattice systems and its dependence on the form of the volume”, Theoret. and Math. Phys., 12:1 (1972), 699–711  mathnet  crossref  mathscinet
    3. G. I. Nazin, “Limit distribution functions in classical statistical physics”, Theoret. and Math. Phys., 21:3 (1974), 1223–1233  mathnet  crossref  mathscinet  zmath
    4. R. L. Dobrushin, “Conditions for the absence of phase transitions in one-dimensional classical systems”, Math. USSR-Sb., 22:1 (1974), 28–48  mathnet  crossref  mathscinet  zmath
    5. R. L. Dobrushin, B. S. Nakhapetian, “Strong convexity of the pressure for lattice systems of classical statistical physics”, Theoret. and Math. Phys., 20:2 (1974), 782–790  mathnet  crossref  mathscinet  zmath
    6. S. N. Lakaev, R. A. Minlos, “Bound states of a cluster operator”, Theoret. and Math. Phys., 39:1 (1979), 336–342  mathnet  crossref  mathscinet
    7. R. L. Dobrushin, “Vlasov equations”, Funct. Anal. Appl., 13:2 (1979), 115–123  mathnet  crossref  mathscinet  zmath
    8. Theoret. and Math. Phys., 45:2 (1980), 1027–1029  mathnet  crossref  mathscinet  isi
    9. V. A. Zagrebnov, “A new proof and generalization of the Bogolyubov–Ruelle theorem”, Theoret. and Math. Phys., 51:3 (1982), 570–579  mathnet  crossref  mathscinet  isi
    10. S. B. Shlosman, “Reflection positivity and models with noncompact spin”, Theoret. and Math. Phys., 59:1 (1984), 421–425  mathnet  crossref  mathscinet  isi
    11. I. G. Brankov, V. A. Zagrebnov, N. S. Tonchev, “Description of limit gibbs states for Curie–Weiss–Ising model”, Theoret. and Math. Phys., 66:1 (1986), 72–80  mathnet  crossref  mathscinet  isi
    12. S. B. Shlosman, “The method of reflection positivity in the mathematical theory of first-order phase transitions”, Russian Math. Surveys, 41:3 (1986), 83–134  mathnet  crossref  mathscinet  adsnasa  isi
    13. V. A. Volevich, “Construction of an analogue of Bowen–Ruelle–Sinai (measure for a multidimensional lattice of interacting hyperbolic mappings”, Russian Acad. Sci. Sb. Math., 79:2 (1994), 347–363  mathnet  crossref  mathscinet  zmath  isi
    14. E. V. Radkevich, “The existence of a Gibbs random field for systems of particles with impulses”, Russian Math. Surveys, 50:6 (1995), 1301–1303  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    15. B. S. Nakhapetian, “Strong convexity of pressure for spin lattice systems”, Russian Math. Surveys, 52:2 (1997), 341–347  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    16. R. A. Minlos, “R. L. Dobrushin – one of the founders of modern mathematical physics”, Russian Math. Surveys, 52:2 (1997), 251–256  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    17. S. A. Albeverio, Yu. G. Kondrat'ev, T. Pasurek, M. Röckner, “Euclidean Gibbs states of quantum crystals”, Mosc. Math. J., 1:3 (2001), 307–313  mathnet  crossref  mathscinet  zmath
    18. I. S. Borisov, “A note on Dobrushin's theorem and couplings in poisson approximation in abelian groups”, Theory Probab. Appl., 48:3 (2004), 521–528  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    19. Khrennikov A.Yu., Mukhamedov F.M., Mendes J.F.F., “On p–adic Gibbs measures of the countable state Potts model on the Cayley tree”, Nonlinearity, 20:12 (2007), 2923–2937  crossref  mathscinet  isi
    20. Proc. Steklov Inst. Math., 265 (2009), 165–176  mathnet  crossref  mathscinet  zmath  isi  elib
    21. Kulik A.M., “Exponential ergodicity of the solutions to SDEs with a jump noise”, Stochastic Processes and Their Applications, 119:2 (2009), 602–632  crossref  mathscinet  zmath  isi
    22. Bogachev L.V., Zarbaliev S.M., “Universality of the Limit Shape of Convex Lattice Polygonal Lines”, Ann Probab, 39:6 (2011), 2271–2317  crossref  isi
    23. V. I. Bogachev, A. V. Kolesnikov, “The Monge–Kantorovich problem: achievements, connections, and perspectives”, Russian Math. Surveys, 67:5 (2012), 785–890  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    24. P. Khe, K. A. Borovkov, “Predelnye teoremy dlya indikatorov rekordov v porogovykh $F^{\alpha}$-skhemakh”, Teoriya veroyatn. i ee primen., 65:3 (2020), 521–537  mathnet  crossref
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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