Symmetric inclusion process with slow boundary: hydrodynamics and hydrostatics

Abstract

We study the hydrodynamic and hydrostatic limits of the one-dimensional open symmetric inclusion process with slow boundary. Depending on the value of the parameter tuning the interaction rate of the bulk of the system with the boundary, we obtain a linear heat equation with either Dirichlet, Robin or Neumann boundary conditions as hydrodynamic equation. In our approach, we combine duality and first-second class particle techniques to reduce the scaling limit of the inclusion process to the limiting behavior of a single, non-interacting, particle.

arXiv comment35 pages, 1 figure. Final version. To appear in Bernoulli

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Cited by in corpus (10)

• Integrable heat conduction model
• Current fluctuations in a semi-infinite line
• Duality in quantum transport models
• Large Deviations in the Symmetric Simple Exclusion Process with Slow Boundaries: A Hydrodynamic Perspective
• Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations
• Hydrodynamical behavior for the generalized symmetric exclusion with open boundary
• Scaling Limits of Random Walks, Harmonic Profiles, and Stationary Non-Equilibrium States in Lipschitz Domains
• Large deviations of current for the symmetric simple exclusion process on a semi-infinite line, and on an infinite line with a slow bond
• Spectral gap of the symmetric inclusion process
• Limits to positional information in boundary-driven systems