May 2022 Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics
Chiara Franceschini, Patrícia Gonçalves, Federico Sau
Author Affiliations +
Bernoulli 28(2): 1340-1381 (May 2022). DOI: 10.3150/21-BEJ1390


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.

Funding Statement

C.F. and P.G. thank FCT/Portugal for support through the project UID/MAT/04459/2013.
This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovative programme (grant agreement No. 715734).
F.S. was founded by the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411.


F.S. wishes to thank Joe P. Chen for some fruitful discussions at an early stage of this work. F.S. thanks CAMGSD, IST, Lisbon, where part of this work has been done, and the European research and innovative programme No. 715734 for the kind hospitality.


Download Citation

Chiara Franceschini. Patrícia Gonçalves. Federico Sau. "Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics." Bernoulli 28 (2) 1340 - 1381, May 2022.


Received: 1 February 2021; Revised: 1 June 2021; Published: May 2022
First available in Project Euclid: 3 March 2022

MathSciNet: MR4388941
zbMATH: 07526587
Digital Object Identifier: 10.3150/21-BEJ1390

Keywords: duality for Markov processes , Hydrodynamic limit , hydrostatic limit , Non-equilibrium steady state , second class particles , slow boundary , symmetric inclusion process

Rights: Copyright © 2022 ISI/BS


This article is only available to subscribers.
It is not available for individual sale.

Vol.28 • No. 2 • May 2022
Back to Top