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Static large deviations for a reaction–diffusion model

Abstract

We consider the superposition of a symmetric simple exclusion dynamics, speeded-up in time, with a spin-flip dynamics in a one-dimensional interval with periodic boundary conditions. We prove the large deviations principle for the empirical measure under the stationary state. We deduce from this result that the stationary state is concentrated on the stationary solutions of the hydrodynamic equation which are stable.

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Notes

  1. 1.

    Note that for N large the set \(\partial B^N\) does not depend on \(\beta _1\).

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Acknowledgements

The authors wish to express their gratitude to the referee for a very careful reading which helped to improve the presentation.

Author information

Correspondence to K. Tsunoda.

Additional information

C. Landim has been partially supported by FAPERJ CNE E-26/201.207/2014, by CNPq Bolsa de Produtividade em Pesquisa PQ 303538/2014-7, and by ANR-15-CE40-0020-01 LSD of the French National Research Agency. K. Tsunoda has been partially supported by Grant-in-Aid for Research Activity Start-up JP16H07041.

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Farfán, J., Landim, C. & Tsunoda, K. Static large deviations for a reaction–diffusion model. Probab. Theory Relat. Fields 174, 49–101 (2019). https://doi.org/10.1007/s00440-018-0858-5

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Keywords

  • Reaction–diffusion equations
  • Hydrostatics
  • Large deviations
  • Nonequilibrium stationary states

Mathematics Subject Classification

  • 82C22
  • 60F10
  • 82C35