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Hydrodynamic limit and density fluctuations of a reaction-diffusion equation

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  • Chen, Ziying
  • Li, Yong

Abstract

We study a class of reaction-diffusion systems based on the symmetric partial exclusion process on a one-dimensional discrete torus, where each site can accommodate up to two particles. For this system, we rigorously derive both the hydrodynamic limit and the hydrostatic limit, and provide quantitative estimates on the law of large numbers under the non-equilibrium steady state. By employing Yau’s relative entropy method and related inequalities, we further demonstrate that the density fluctuations around the hydrostatic limit are described by an infinite-dimensional Ornstein-Uhlenbeck process. This result establishes a central limit theorem for the density of particles under the non-equilibrium stationary states, characterizing the asymptotic behavior of fluctuations in the macroscopic regime.

Suggested Citation

  • Chen, Ziying & Li, Yong, 2026. "Hydrodynamic limit and density fluctuations of a reaction-diffusion equation," Stochastic Processes and their Applications, Elsevier, vol. 201(C).
    • Handle: RePEc:eee:spapps:v:201:y:2026:i:c:s0304414926001912
    DOI: 10.1016/j.spa.2026.105059
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