Advertisement

Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

An ergodic theorem for interacting systems with attractive interactions

  • 66 Accesses

  • 27 Citations

This is a preview of subscription content, log in to check access.

References

  1. 1.

    Dobrušin, R. L.: Markov processes with a large number of locally interacting components — existence of the limiting process and its ergodicity. Probl. Peredači Inform.7, 2, 70–87 (1971).

  2. 2.

    Dobrušin, R.L.: The problem of uniqueness of a Gibbsian random field and the problem of phase transitions. Funkcional'. Analiz. PriloŽenija2, 302–312 (1968).

  3. 3.

    Felderhof, B. U.: Spin relaxation of the Ising chain. Rep. Math. Phys.1, 215–234 (1970).

  4. 4.

    Harris,T.E.: Nearest-neighbor Markov interaction processes on multidimensional lattices. To appear in Advances Math.

  5. 5.

    Holley, R.: A class of interactions in an infinite particle system. Advances Math.5, 291–309 (1970).

  6. 6.

    Holley, R.: Markovian interaction processes with finite range interactions. To appear in Ann. Math. Statistics.

  7. 7.

    Liggett, T.M.: Existence theorems for infinite particle systems. Trans. Amer. Math. Soc.165, 471–481 (1972).

  8. 8.

    Ruelle, D., to appear.

  9. 9.

    Spitzer, F.: Interaction of Markov processes. Advances Math.5, 246–290 (1970).

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Holley, R. An ergodic theorem for interacting systems with attractive interactions. Z. Wahrscheinlichkeitstheorie verw Gebiete 24, 325–334 (1972). https://doi.org/10.1007/BF00679137

Download citation

Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Attractive Interaction
  • Ergodic Theorem