L2 theory for the stochastic Ising model

  • R. A. Holley
  • D. W. Stroock


Stochastic Process Probability Theory Mathematical Biology 
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  1. 1.
    Dobrushin, R. L.: Gibbsian random fields for lattice systems with pairwise interactions. Functional Anal. Appl. 2, 292–302 (1968)Google Scholar
  2. 2.
    Glauber, R. J.: Time dependent statistics of the Ising model. J. Math. Phys. 4, 294–307 (1963)Google Scholar
  3. 3.
    Higuchi, Y., Shiga, T.: Some results on Markov processes of infinite lattice spin systems. J. Math. Kyota Univ. 15, 211–229 (1975)Google Scholar
  4. 4.
    Holley, R.: Recent results on the stochastic Ising model. Rocky Moantain J. Math. 4, 479–496 (1974)Google Scholar
  5. 5.
    Holley, R., Stroock, D.: A martingale approach to infinite systems of interacting processes. [To appear in Ann. Probab.]Google Scholar
  6. 6.
    Kaufman, B., Onsager, L.: Crystal Statistics III. Short range order in a binary Ising lattice. Phys. Rev. 76, 1244–1252 (1949)Google Scholar
  7. 7.
    Lebowitz, J. L.: Bounds on the correlation and analyticity properties of ferromagnetic Ising spin systems. In pressGoogle Scholar
  8. 8.
    Marinaro, M., Sewell, G. L.: Characterizations of phase transitions in Ising spin systems. Comm. Math. Phys. 24, 310–335 (1972)Google Scholar
  9. 9.
    Sullivan, W. G.: Mean square relaxation times for evolution of random fields. Comm. Math. Phys. 40, 249–258 (1975)Google Scholar
  10. 10.
    Sullivan, W. G.: A unified existence and ergodic theorem for Markov evaluation of random fields. Z. Wahrscheinlichkeitstheorie verw. Gebiete 31, 47–56 (1974)Google Scholar
  11. 11.
    Sullivan, W. G.: Processes with infinitely many jumping particles. [To appear in Proc. Amer. Math. Soc.]Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • R. A. Holley
    • 1
  • D. W. Stroock
    • 1
  1. 1.Mathematics Dept.University of ColoradoBoulderUSA

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