Hydrodynamic Limit of the Symmetric Zero-Range Process with Slow Boundary

2025/08/26 by Araújo, Oslenne, Gonçalves, Patrícia, Neumann, Adriana +1
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2508.19447

Abstract

We study the hydrodynamic behaviour of the symmetric zero-range process on the finite interval \1, …, 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≥1. 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.

Citations

• A consistency-stability approach to scaling limits of zero-range processes
• Non-equilibrium steady state of the symmetric exclusion process with reservoirs
• Hydrodynamic limit for a boundary driven super-diffusive symmetric exclusion
• Diffusive to super-diffusive behavior in boundary driven exclusion
• Hydrodynamics for symmetric exclusion in contact with reservoirs
• A microscopic model for a one parameter class of fractional laplacians with dirichlet boundary conditions
• Non-equilibrium and stationary fluctuations of a slowed boundary\n symmetric exclusion
• Equilibrium fluctuations for the slow boundary exclusion process

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