Bernoulli and Markov stationary measures in discrete local interactions

  • N. B. Vasilyev
Part II
Part of the Lecture Notes in Mathematics book series (LNM, volume 653)


Markov Chain Stationary Measure Transition Function Gibbs Measure Markov Random Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Belyaev Y.K., Gromak Y.I., and Malishev V.A. On invariant random boolean fields. Mat. Zametki (Russian) 6 (1969), 555–566.MathSciNetzbMATHGoogle Scholar
  2. 2.
    Dawson D.A., Information flow in some classes of Markov systems. J.App.Probability 10 (1973), 63–83; and II (1974).CrossRefzbMATHGoogle Scholar
  3. 3.
    Dawson D.A. Information flow in graphs. Stochastic Processes Appl. 3 (1975), 137–151.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Dawson D.A. Synchronous and asynchronous reversible Markov systems. Canad.Math.Bull., 17 (1975) (5), 633–649.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Dobrushin R.L. Markov processes with a large number of local interact components. Problemy Peredači Informacii (Russian) 7 (1971), vyp.2, 70–87 and vyp. 3, 57–66.Google Scholar
  6. 6.
    Harris T.E. Contact interactions on a lattice. Ann.Probability 2, (1974), 969–988.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Holley R. Free energy in a Markovian model of a lattice spin system Comm.Math.Phys. 23 (1971), 87–99.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Holley R. An ergodic theorem for interacting with attractive interactions. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 24 (1972), 325–334.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Holley R. and Ligget T. Ergodic theorems for weakly interacting system and the voter model. Ann. Probability 3 (1975), 643–663.MathSciNetCrossRefGoogle Scholar
  10. 10.
    Holley R.A. and Stroock D.W. L2-theory for the stochastic Ising model. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 35 (1976), 87–101.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Preston C.J. Random Fields. Oxford Lecture Notes, 1975.Google Scholar
  12. 12.
    Shmukler Yulia. The problem of voting with random error. Dokl.Acad. Nauk SSSR (Russian) 196 (1971).Google Scholar
  13. 13.
    Sullivan W.G. Markov Processes for Random Fields. Comm. Dublin Inst. Adv. Studies series A, no 23, 1975.Google Scholar
  14. 14.
    Vaserstein L.N. Markov processes on countable products of spaces, describing large systems of automata. Problemy Peredači Informacii (Russian) 5(1969), vyp.3, 64–72.MathSciNetzbMATHGoogle Scholar
  15. 15.
    Vaserstein L.N. and Leontovich A.M. On invariant measures of some Markov operators describing a homogeneous random network. Problemy Peredači Informacii (Russian) 6 (1970), vyp.1, 71–80.Google Scholar
  16. 16.
    Vasilyev N.B., Petrovskaya M.B. and Pyatetsky-Shapiro I.I. A model of voting with random errors. Avtomat. i Telemeh. (Russian) no 10, (1969), 103–107.Google Scholar
  17. 17.
    Vasilyev N.B. and Kozlov O.K. Reversible Markov chains with local interaction. To appear in "Multicomponent Stochastic Systems" (Russian) M.Nauka, 1977.Google Scholar
  18. 18.
    Vasilyev A.V. Investigation of stationary probability of a Markov interaction system. Problemy Peredači Informacii (Russian) 11(1975) vyp.4.Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • N. B. Vasilyev
    • 1
  1. 1.Moscow UniversityRussia

Personalised recommendations