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Stochastic Burgers equation from long range exclusion interactions

Author

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  • Gonçalves, Patrícia
  • Jara, Milton

Abstract

We consider one-dimensional exclusion processes with long jumps given by a transition probability of the form pn(⋅)=s(⋅)+γna(⋅), such that its symmetric part s(⋅) is irreducible with finite variance and its antisymmetric part is absolutely bounded by s(⋅). We prove that under diffusive time scaling and strength of asymmetry nγn→n→∞b≠0, the equilibrium density fluctuations are given by the unique energy solution of the stochastic Burgers equation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:12:p:4029-4052
    DOI: 10.1016/j.spa.2017.03.022
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    Cited by:

    1. 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).

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