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

19.01.2022 14:00 - 14:45

Lorenzo Dello Schiavo (IST Austria)

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.


SFB 65, DK

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