Journal of Statistical Physics

, Volume 147, Issue 3, pp 519–528 | Cite as

Non-equilibrium Stationary States in the Symmetric Simple Exclusion with Births and Deaths

  • Anna De Masi
  • Errico Presutti
  • Dimitrios Tsagkarogiannis
  • Maria Eulalia Vares


We consider the symmetric simple exclusion process in the interval Λ N :=[−N,N]∩ℤ with births and deaths taking place respectively on suitable boundary intervals I + and I , as introduced in De Masi et al. (J. Stat. Phys. 144:1151–1170, 2011). We study the stationary measure and its macroscopic density profile in the limit N→∞.


Interacting particle systems Hydrodynamic limit 



This work has been partially supported by the PRIN project, n. 2009TA2595. M.E.V. thanks the Universities of Rome and L’Aquila for kind hospitality. M.E.V. is partially supported by CNPq grant 302796/2002-9. The research of D.T. has been partially supported by a Marie Curie Intra European Fellowship within the 7th European Community Framework Program.


  1. 1.
    De Masi, A., Presutti, E., Tsagkarogiannis, D., Vares, M.E.: Current reservoirs in the simple exclusion process. J. Stat. Phys. 144, 1151–1170 (2011) MathSciNetADSMATHCrossRefGoogle Scholar
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    De Masi, A., Presutti, E., Tsagkarogiannis, D., Vares, M.E.: Truncated correlations in the stirring process with births and deaths. Electron. J. Probab. 17(6), 1–35 (2012) Google Scholar
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    Liggett, T.M.: Interacting Particle Systems. A Series of Comprehensive Studies in Mathematics, vol. 276. Springer, Berlin (1985) MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Anna De Masi
    • 1
  • Errico Presutti
    • 2
  • Dimitrios Tsagkarogiannis
    • 2
  • Maria Eulalia Vares
    • 3
  1. 1.Dipartimento di MatematicaUniversità di L’AquilaL’AquilaItaly
  2. 2.Dipartimento di MatematicaUniversità di Roma Tor VergataRomaItaly
  3. 3.Instituto de MatemáticaUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil

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