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 / Franceschini, C.; Goncalves, P.; Sau, F.. - In: BERNOULLI. - ISSN 1350-7265. - 28:2(2022), pp. 1340-1381. [10.3150/21-BEJ1390]

Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics

Franceschini C.;
2022

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
28
2
1340
1381
Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics / Franceschini, C.; Goncalves, P.; Sau, F.. - In: BERNOULLI. - ISSN 1350-7265. - 28:2(2022), pp. 1340-1381. [10.3150/21-BEJ1390]
Franceschini, C.; Goncalves, P.; Sau, F.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1288886
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