An ergodic theorem for a class of spin systems

David Griffeath

Annales de l'I.H.P. Probabilités et statistiques (1977)

  • Volume: 13, Issue: 2, page 141-157
  • ISSN: 0246-0203

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Griffeath, David. "An ergodic theorem for a class of spin systems." Annales de l'I.H.P. Probabilités et statistiques 13.2 (1977): 141-157. <http://eudml.org/doc/77059>.

@article{Griffeath1977,
author = {Griffeath, David},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
language = {eng},
number = {2},
pages = {141-157},
publisher = {Gauthier-Villars},
title = {An ergodic theorem for a class of spin systems},
url = {http://eudml.org/doc/77059},
volume = {13},
year = {1977},
}

TY - JOUR
AU - Griffeath, David
TI - An ergodic theorem for a class of spin systems
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1977
PB - Gauthier-Villars
VL - 13
IS - 2
SP - 141
EP - 157
LA - eng
UR - http://eudml.org/doc/77059
ER -

References

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  1. [1] L. Gray, D. Griffeath, On the uniqueness of certain interacting particle systems. Z. Wahr. verw. Geb., t. 35, 1976, p. 75-86. Zbl0316.60067MR405643
  2. [2] T.E. Harris, On a class of set-valued Markov processes. Ann. Probab., t. 4, 1976, p. 175-194. Zbl0357.60049MR400468
  3. [3] R. Holley, T. Liggett, Ergodic theorems for weakly interacting infinite systems and the voter model. Ann. Probab., t. 3, 1975, p. 643-663. Zbl0367.60115MR402985
  4. [4] R. Holley, D. Stroock, A martingale approach to infinite systems of interacting processes. Ann. Probab., t. 4, 1976, p. 195-228. Zbl0332.60072MR397927
  5. [5] R. Holley, D. Stroock, Dual processes and their application to infinite interacting systems. Adv. Math. To appear, 1976. Zbl0459.60097
  6. [6] R. Holley, D. Stroock, D. Williams, Applications of dual processes to diffusion theory. Proc. Symposia Pure Math. To appear, 1977. Zbl0382.60081MR443110
  7. [7] T.M. Liggett, Existence theorems for infinite particle systems. Trans. Amer. Math. Soc., t. 165, 1972, p. 471-481. Zbl0239.60072MR309218
  8. [8] N.S. Matloff, Equilibrium behavior in an infinite voting model. Ph. D. thesis, U.C.L.A., 1975. 
  9. [9] D. Schwartz, Ergodic theorems for an infinite particle system with sinks and sources. Ph. D. thesis, U. C. L. A., 1975. 
  10. [10] D. Schwartz, Applications of duality to a class of Markov processes. Ann. Probab. To appear, 1976. Zbl0367.60111MR448631
  11. [11] A.L. Toom, Nonergodic multidimensional systems of automata. Problemy Peredachi Informatsii, t. 10, no. 3, 1974, p. 229-246. Zbl0315.94053MR469584
  12. [12] L.N. Vasershtein, A.M. Leontovich, Invariant measures of certain Markov operators describing a homogeneous random medium. Problemy Peredachi Informatsii, t. 6, no. 1, 1970, p. 71-80. MR530400
  13. [13] N.B. Vasil'ev, M.B. Petrovskaya, I.I. Piatetskii-Shapiro, Modelling of voting with random error. Avtomatika i Telemekhanika, t. 10, 1969, p. 103-107. Zbl0205.17803
  14. [14] N.B. Vasil'ev, I.I. Piatetskii-Shapiro, On the classification of one-dimensional homogeneous networks. Problemy Peredachi Informatsii, t. 7, no. 4, 1971, p. 82-90. Zbl0306.94030MR309672

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