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

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Abstract

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.

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Authors and Affiliations

  1. Faculdade de Filosofia Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, Ribeirão Preto, Brazil

    G. G. Bosco

  2. Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brazil

    F. P. Machado

  3. Universidade Federal do ABC, Santo André, Brazil

    Thomas Logan Ritchie

Authors
  1. G. G. Bosco
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  2. F. P. Machado
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  3. Thomas Logan Ritchie
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Corresponding author

Correspondence to G. G. Bosco.

Additional information

G.G. Bosco is supported by a grant from Capes.

T.L. Ritchie is supported by grants from CNPq and Fapesp.

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Bosco, G.G., Machado, F.P. & Ritchie, T.L. Exponential Rates of Convergence in the Ergodic Theorem: A Constructive Approach. J Stat Phys 139, 367–374 (2010). https://doi.org/10.1007/s10955-010-9945-4

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  • DOI: https://doi.org/10.1007/s10955-010-9945-4

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