Calculus of Variations and Geometric Measure Theory

L. Dello Schiavo - L. Portinale - F. Sau

Scaling Limits of Random Walks, Harmonic Profiles, and Stationary Non-Equilibrium States in Lipschitz Domains

created by portinale on 17 Oct 2023
modified on 26 Feb 2024


Accepted Paper

Inserted: 17 oct 2023
Last Updated: 26 feb 2024

Journal: To appear in Annals of Applied Probability
Year: 2021

ArXiv: 2112.14196 PDF


We consider the open symmetric exclusion (SEP) and inclusion (SIP) processes on a bounded Lipschitz domain $\Omega$, with both fast and slow boundary. For the random walks on $\Omega$ dual to SEPSIP we establish: a functional-CLT-type convergence to the Brownian motion on $\Omega$ 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 SEPSIP on $\Omega$, and analyze their stationary non-equilibrium fluctuations. All scaling limit results for SEPSIP concern finite-dimensional distribution convergence only, as our duality techniques do not require to establish tightness for the fields associated to the particle systems.