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

  • Thomas Mountford
  • Glauco Valle
Article
  • 15 Downloads

Abstract

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.

Keywords

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

Mathematics Subject Classification (2010)

60K35 

Notes

Acknowledgements

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

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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