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Hydrodynamic Limit of the Symmetric Zero-Range Process with Slow Boundary
Oslenne Araújo, Patrícia Gonçalves, Adriana Neumann, Maria Chiar · 2025-08-27 · via math.PR updates on arXiv.org

We study the hydrodynamic behaviour of the symmetric zero-range process on the finite interval $\{1, \ldots, N-1\}$ in contact with slow reservoirs at the boundary. Particles are injected and removed at sites $1$ and $N-1$ at rates that scale like $N^{-θ}$ with $θ\ge1$. Under mild assumptions on the jump rate and the sequence of initial measures, we show that the empirical density evolves on the diffusive scale according to a nonlinear heat equation, with boundary conditions reflecting the strength of the reservoirs.

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