Scaling limits of boundary-driven interacting particle systems and random walks on Lipschitz domains

Portinale Lorenzo, Hausdorff Center for Mathematics, Bonn

In this talk, we discuss random walks on (possibly random) discretizations of a Lipschitz domain $\Omega$ with boundary interaction in a (possibly random) non trivial environment. We provide a general framework to show convergence of the associated processes to a continuous diffusion into three different regimes of interaction with the boundary, either Neumann (slow boundary), Dirichlet (fast boundary), or Robin (at criticality) boundary conditions, as well as the discrete-to-continuum convergence of the corresponding harmonic profiles. Via a duality argument, a corollary of our result is e.g. the hydrodynamic and hydrostatic limits for SEP/SIP on $\Omega$, and the analysis of their stationary non-equilibrium fluctuations. Several examples will be discussed. This is based on a collaboration with L. Dello Schiavo, S. Floreani, and F. Sau.

Area: CS43 - Hydrodynamic limits (Simone Floreani)

Keywords: Randomm walk, Lipschitz domain, random environment, homogenization, hydrodynamic limits.

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