Martedì 10 Gennaio 2023, ore 14:00
Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
*Speaker: *Lorenzo Dello Schiavo (ISTA, Vienna)
*Titolo:* Scaling Limits of Random Walks, Harmonic Profiles, and Stationary
Non-Equilibrium States in Lipschitz Domains
*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. We further show 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 arXiv:2112.14196 with Lorenzo Portinale
(IAM Bonn) and Federico Sau (ISTA)