@article{15317,
  abstract     = {We consider the open symmetric exclusion (SEP) and inclusion (SIP) processes on a bounded Lipschitz domain Ω, with both fast and slow boundary. For the random walks on Ω dual to SEP/SIP we establish: a functional-CLT-type convergence to the Brownian motion on Ω with either Neumann (slow boundary), Dirichlet (fast boundary), or Robin (at criticality) boundary conditions; the discrete-to-continuum convergence of the corresponding harmonic profiles. As a consequence, we rigorously derive the hydrodynamic and hydrostatic limits for SEP/SIP on Ω, and analyze their stationary nonequilibrium fluctuations. All scaling limit results for SEP/SIP concern finite-dimensional distribution convergence only, as our duality techniques do not require to establish tightness for the fields associated to the particle systems.},
  author       = {Dello Schiavo, Lorenzo and Portinale, Lorenzo and Sau, Federico},
  issn         = {1050-5164},
  journal      = {Annals of Applied Probability},
  number       = {2},
  pages        = {1789--1845},
  publisher    = {Institute of Mathematical Statistics},
  title        = {{Scaling limits of random walks, harmonic profiles, and stationary nonequilibrium states in Lipschitz domains}},
  doi          = {10.1214/23-AAP2007},
  volume       = {34},
  year         = {2024},
}