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arXiv · 2007.11998

Symmetric inclusion process with slow boundary: hydrodynamics and hydrostatics

Chiara Franceschini·Patrícia Gonçalves·Federico Sau
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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.

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Chiara Franceschini, Patrícia Gonçalves, Federico Sau. 2020-07-23. Symmetric inclusion process with slow boundary: hydrodynamics and hydrostatics. https://doi.org/10.3150/21-bej1390

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