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.

Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics

Sau, F
2022-01-01

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.
2022
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https://projecteuclid.org/journals/bernoulli/volume-28/issue-2/Symmetric-inclusion-process-with-slow-boundary-Hydrodynamics-and-hydrostatics/10.3150/21-BEJ1390.full
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/3043503
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