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Fluctuations of empirical means at low temperature for finite Markov chains with rare transitions in the general case
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  • Published: June 1998

Fluctuations of empirical means at low temperature for finite Markov chains with rare transitions in the general case

  • Isabelle Gaudron1 &
  • Alain Trouvé2 

Probability Theory and Related Fields volume 111, pages 215–251 (1998)Cite this article

Summary.

The integrated autocovariance and autocorrelation time are essential tools to understand the dynamical behavior of a Markov chain. We study here these two objects for Markov chains with rare transitions with no reversibility assumption. We give upper bounds for the autocovariance and the integrated autocorrelation time, as well as exponential equivalents at low temperature. We also link their slowest modes with the underline energy landscape under mild assumptions. Our proofs will be based on large deviation estimates coming from the theory of Wentzell and Freidlin and others [4, 3, 12], and on coupling arguments (see [6] for a review on the coupling method).

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Authors and Affiliations

  1. CMLA, Ecole Normale Supérieure de Cachan 61, Av. du Président Wilson, F-94235 Cachan Cedex France, , , , , , FR

    Isabelle Gaudron

  2. Université Paris 13, LAGA, UMR 7539, Avenue Jean-Baptiste Clément, F-93430 Villetaneuse, France, , , , , , FR

    Alain Trouvé

Authors
  1. Isabelle Gaudron
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  2. Alain Trouvé
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Received 5 August 1996 / In revised form: 6 August 1997

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Gaudron, I., Trouvé, A. Fluctuations of empirical means at low temperature for finite Markov chains with rare transitions in the general case. Probab Theory Relat Fields 111, 215–251 (1998). https://doi.org/10.1007/s004400050167

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  • Issue Date: June 1998

  • DOI: https://doi.org/10.1007/s004400050167

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  • Mathematics Subject Classification (1991): 60F05
  • 60F10
  • 60J10
  • 60M10
  • 65C05
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