Communications in Mathematical Physics

, Volume 123, Issue 1, pp 85–93 | Cite as

Uniform andL2 convergence in one dimensional stochastic Ising models

  • Richard A. Holley
  • Daniel W. Stroock


We study the rate of convergence to equilibrium of one dimensional stochastic Ising models with finite range interactions. We donot assume that the interactions are ferromagnetic or that the flip rates are attractive. The infinitesimal generators of these processes all have gaps between zero and the rest of their spectra. We prove that if one of these processes is observed by means of local observables, then the convergence is seen to be exponentially fast with an exponent that is any number less than the spectral gap. Moreover this exponential convergence is uniform in the initial configuration.


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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Richard A. Holley
    • 1
    • 2
  • Daniel W. Stroock
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of ColoradoBoulderUSA
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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