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Diffusive fluctuations of long-range symmetric exclusion with a slow barrier

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  • Cardoso, Pedro
  • Gonçalves, Patrícia
  • Jiménez-Oviedo, Byron

Abstract

In this article we obtain the equilibrium fluctuations of a symmetric exclusion process in Z with long jumps. The transition probability of the jump from x to y is proportional to |x−y|−γ−1. Here we restrict to the choice γ≥2 so that the system has a diffusive behaviour. Moreover, when particles move between negative integers sites and sites in N, the jump rates are slowed down by a factor αn−β, where α>0, β≥0 and n is the scaling parameter. Depending on the values of β and γ, we obtain several stochastic partial differential equations, corresponding to a heat equation without boundary conditions, or with Robin boundary conditions or Neumann boundary conditions.

Suggested Citation

  • Cardoso, Pedro & Gonçalves, Patrícia & Jiménez-Oviedo, Byron, 2023. "Diffusive fluctuations of long-range symmetric exclusion with a slow barrier," Stochastic Processes and their Applications, Elsevier, vol. 166(C).
    • Handle: RePEc:eee:spapps:v:166:y:2023:i:c:s0304414923001874
    DOI: 10.1016/j.spa.2023.09.010
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    References listed on IDEAS

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    1. Gonçalves, Patrícia & Jara, Milton, 2017. "Stochastic Burgers equation from long range exclusion interactions," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 4029-4052.
    2. Franco, Tertuliano & Gonçalves, Patrícia & Neumann, Adriana, 2013. "Phase transition in equilibrium fluctuations of symmetric slowed exclusion," Stochastic Processes and their Applications, Elsevier, vol. 123(12), pages 4156-4185.
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