Hydrostatic Limit and Fick’s Law for the Symmetric Exclusion with Long Jumps

  • Byron Jiménez OviedoEmail author
  • Arthur VavasseurEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 258)


Hydrostatic behavior and Fick’s law for the one dimensional exclusion process with long jumps in contact with infinite reservoirs at different densities are derived. The jump rate is described by a transition probability p which is proportional to \(\vert \cdot \vert ^{-(\gamma +1)}\) for \(\gamma >2\). The reservoirs add or remove particles with rate proportional to \(\kappa N^{-\theta }\), where \(\kappa >0\) and \(\theta =2-\gamma \). The behavior of the solution of the hydrostatic equation is also studied.



The authors are very grateful to Cédric Bernardin and Patrícia Gonçalves for useful discussions and suggestions. Byron Jiménez Oviedo thanks Universidad Nacional de Costa Rica, L’institut Français d’Amérique centrale-IFAC for financial support through his Ph.D. grant and the Program Pessoa of Cooperation between Portugal and France with reference 406/4/4/2017/S.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Laboratoire J.A Dieudonné, CNRSUniversité de Nice Sophia-AntipolisNice Cedex 02France

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