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On K-systems and Bernoullicity in statistical mechanics

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Théorie Ergodique

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 532))

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References

  1. R. L. Dobrushin. Th. Prob. Appl. 13, (1968), 197–224.

    Article  Google Scholar 

  2. W. G. Sullivan. Comm. Math. Phys. 33, (1973), 61–74. See also M. B. Averintzev: Prob. Peredach. Inf. 6, (1970), 100–109; M. B. Averintzev: Th. Prob. Appl. 17, (1972). F. Spitzer: Am. Math. Monthly 78, (1972), 142. C. J. Preston: Adv. Appl. Prob. 5, (1973), 242–261.

    Article  MathSciNet  Google Scholar 

  3. D. E. Lanford and D. Ruelle. Comm. Math. Phys. 13, (1969), 194–215.

    Article  MathSciNet  Google Scholar 

  4. D. Ruelle. Cargèse Lectures on Physics, (1969), edited by D. Kastler.

    Google Scholar 

  5. R. L. Dobrushin. Functional Anal. Appl. 2, (1968), 302–312.

    Article  Google Scholar 

  6. F. di Liberto. Comm. Math. Phys. 29, (1973), 293–310.

    Article  MathSciNet  Google Scholar 

  7. G. Gallavotti and S. Miracle-Solé. Phys. Rev. 85, (1972), 2555–2559

    Article  Google Scholar 

  8. D. Ruelle. Ann. Phys. 69, (1972), 364.

    Article  Google Scholar 

  9. J. L. Lebowitz and A. Martin-Löf. Comm. Math. Phys., (1972), 25

    Google Scholar 

  10. D. Ruelle. Phys. Rev. Letters 26, (1971), 303–304

    Article  MathSciNet  Google Scholar 

  11. G. Gallavotti and S. Miracle-Solé. Comm. Math. Phys. 7, (1968), 274–288

    Article  MathSciNet  Google Scholar 

  12. D. Ruelle. Comm. Math. Phys. 9, (1968), 267–279

    Article  MathSciNet  Google Scholar 

  13. H. Rost. Private communication. For the case a <3/2 see C. J. Preston: Gibbs states on countable sets (forthcoming), Oxford Univ. Press (1973)

    Google Scholar 

  14. E. J. Dyson. Comm. Math. Phys. 12, (1969), 212–215

    Article  MathSciNet  Google Scholar 

  15. N. A. Friedman and D. S. Ornstein. Adv. Math. 5, (1970), 365–394

    Article  MathSciNet  Google Scholar 

  16. R. L. Dobrushin. Functional Anal. Appl. 2, (1968), 292–301

    Article  Google Scholar 

  17. R. B. Griffith. J. Math. Phys. 8, (1967), 478–489; for a short proof see j. Ginibre. Phys. Rev. Letters 23, (1969), 828–830

    Article  Google Scholar 

  18. R. B. Griffith and D. Ruelle. Comm. Math. Phys. 23, (1971), 169–175. See also A. Martin-Löf. Comm. Math. Phys. 32, (1973), 75–92

    Article  MathSciNet  Google Scholar 

  19. F. Spitzer. Random Fields and Interacting Particle Systems. Math. Assoc. of America, (1971)

    Google Scholar 

  20. G. Gallavotti. Comm. Math. Phys. 32, (1973), 183–190

    Article  MathSciNet  Google Scholar 

  21. F. Ledrappier. Comm. Math. Phys. 33, (1973), 119–128

    Article  MathSciNet  Google Scholar 

  22. F. di Liberto, G. Gallavotti and L. Russo. Comm. Math. Phys. 33, (1973), 259–282

    Article  MathSciNet  Google Scholar 

  23. D. S. Ornstein. Ergodic theory, randomness, and dynamical systems, Stanford (1972)

    Google Scholar 

  24. Y. Katznelson and B. Weiss. Israel J. Math. 12, (1972), 161–173

    Article  MathSciNet  Google Scholar 

  25. D. S. Ornstein. Adv. Math. 5, (1970), 339–348

    Article  MathSciNet  Google Scholar 

  26. R. L. Dobrushin. Theor. Mat. Fjz. 12, (1972), 115

    Google Scholar 

  27. D. Ruelle. Rev. Mod. Phys. 36, (1964), 580–584

    Article  MathSciNet  Google Scholar 

  28. R. Holley. Remarks on the FKG inequalities (preprint 1972); see also the article by A. Brunel in this volume.

    Google Scholar 

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Jean-Pierre Conze Michael S. Keane

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© 1976 Springer-Verlag

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Georgii, HO. (1976). On K-systems and Bernoullicity in statistical mechanics. In: Conze, JP., Keane, M.S. (eds) Théorie Ergodique. Lecture Notes in Mathematics, vol 532. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080182

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  • DOI: https://doi.org/10.1007/BFb0080182

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07803-6

  • Online ISBN: 978-3-540-38217-1

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