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-Central-Limit-Theorem-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 non-equilibrium fluctuations.
Based on joint work with L. Portinale (IAM Bonn) and Federico Sau (IST Austria), arXiv:2112.14196.
Scaling Limits of Random Walks, Harmonic Profiles, and Stationary Non-Equilibrium States in Lipschitz Domains
19.01.2022 14:00 - 14:45
Organiser:
SFB 65, DK
Location:
Zoom Meeting
Related Files
- pde_afternoon_2022-01-19.pdf 599 KB