Journal of Statistical Physics

, Volume 139, Issue 3, pp 367–374 | Cite as

Exponential Rates of Convergence in the Ergodic Theorem: A Constructive Approach

  • G. G. Bosco
  • F. P. Machado
  • Thomas Logan Ritchie


We prove that, once an algorithm of perfect simulation for a stationary and ergodic random field F taking values in \(S^{\mathbb{Z}^{d}}\), S a bounded subset of R n , is provided, the speed of convergence in the mean ergodic theorem occurs exponentially fast for F. Applications from (non-equilibrium) statistical mechanics and interacting particle systems are presented.


Exponential rates Ergodic theorem Random fields Perfect simulation 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • G. G. Bosco
    • 1
  • F. P. Machado
    • 2
  • Thomas Logan Ritchie
    • 3
  1. 1.Faculdade de Filosofia Ciências e Letras de Ribeirão PretoUniversidade de São PauloRibeirão PretoBrazil
  2. 2.Instituto de Matemática e EstatísticaUniversidade de São PauloSão PauloBrazil
  3. 3.Universidade Federal do ABCSanto AndréBrazil

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