2021/12/28 by Lorenzo Dello Schiavo, Lorenzo Portinale, Federico Sau · 1 voice
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Geometry #Harmonic #Lipschitz continuity #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Non-equilibrium thermodynamics #Physics #Quantum mechanics #Random walk #Scaling #Stationary state #Statistical physics #Statistics #advanced mathematical theories #math.PR
paper · pdf · doi:10.1214/23-aap2007
arxiv published 2021/12/28 · arxiv updated 2023/08/03 · openalex publication_date 2024/04/01 · openalex created_date 2024/04/05 · openalex updated_date 2026/06/11
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; 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 nonequilibrium fluctuations. All scaling limit results for SEP/SIP concern finite-dimensional distribution convergence only, as our duality techniques do not require to establish tightness for the fields associated to the particle systems.