Journal of Theoretical Probability

, Volume 32, Issue 1, pp 282–302 | Cite as

Exponential Convergence for the Fredrickson–Andersen One-Spin Facilitated Model

  • Thomas Mountford
  • Glauco ValleEmail author


We prove exponential convergence to equilibrium for the Fredrickson–Andersen one-spin facilitated model on bounded degree graphs satisfying a subexponential, but larger than polynomial, growth condition. This was a classical conjecture related to non-attractive spin systems. Our proof relies on coupling techniques based on Harris graphical construction for interacting particle systems.


Fredrickson–Andersen model Non-attractive Spin system Convergence to equilibrium 

Mathematics Subject Classification (2010)




We would like to thank the anonymous referee for all the useful comments. G. Valle was supported by CNPq Grant 305805/2015-0 and Universal CNPq project 482519/2012-6. Both authors were supported by CNPq Science without Borders Grant 402215/2012-5.


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Authors and Affiliations

  1. 1.Département de MathématiquesÉcole Polytechnique FédéraleLausanneSwitzerland
  2. 2.Instituto de MatemáticaUniversidade Federal do Rio de JaneiroRio de JaneiroBrasil

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