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Communications in Mathematical Physics

, Volume 40, Issue 3, pp 249–258 | Cite as

Mean square relaxation times for evolution of random fields

  • Wayne G. Sullivan
Article

Abstract

We consider the problem of relaxation times for Markov evolution of systems composed of a countable number of locally interacting particles, each one of which has a finite phase space. We give a theorem for comparison of mean square relaxation times of evolutions possessing the same ergodic stationary state. We give a reduction theorem for “attractive” evolutions. The results are applied to a generalization of the Glauber evolution of the one dimensional Ising chain.

Keywords

Neural Network Statistical Physic Relaxation Time Phase Space Complex System 
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.

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References

  1. 1.
    Dobrushin, R. L.: Theory Probability Appl.13, 197–224 (1968)Google Scholar
  2. 2.
    Dobrushin, R. L.: Problems of Information Transmission7, 149–64;7, 235–241 (1971)Google Scholar
  3. 3.
    Doob, J. L.: Stochastic Processes, New York: John Wiley & Sons 1953Google Scholar
  4. 4.
    Felderhof, B. U.: Rep. Math. Phys.1, 215–234 (1970);2, 151–152 (1971)Google Scholar
  5. 5.
    Glauber, R. J.: J. Math. Phys.4, 294–207 (1963)Google Scholar
  6. 6.
    Holley, R.: Z. Wahrscheinlichkeitstheorie verw. Geb.24, 325–334 (1972)Google Scholar
  7. 7.
    Liggett, T. M.: Trans. Am. Math. Soc.165, 471–481 (1972)Google Scholar
  8. 8.
    Preston, C. J.: Specification of random fields I and II. To appear.Google Scholar
  9. 9.
    Sullivan, W. G.: Commun. math. Phys.33, 61–74 (1973)Google Scholar
  10. 10.
    Sullivan, W. G.: A unified existence and ergodic theorem for Markov evolution of random fields. To appearGoogle Scholar
  11. 11.
    Yosida, K.: Functional Analysis. Berlin-Heidelberg-New York: Springer 1965Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • Wayne G. Sullivan
    • 1
  1. 1.Dublin Institute for Advanced StudiesDublinIreland

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