Scaling limits of random walks, harmonic profiles, and stationary nonequilibrium states in Lipschitz domains
Dello Schiavo L, Portinale L, Sau F. 2024. Scaling limits of random walks, harmonic profiles, and stationary nonequilibrium states in Lipschitz domains. Annals of Applied Probability. 34(2), 1789–1845.
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Grant
Taming Complexity in Partial Differential Systems
Optimal Transport and Stochastic Dynamics
Reaching consensus in heterogeneous random opinion dynamics
ISTplus - Postdoctoral Fellowships
Configuration Spaces over Non-Smooth Spaces
Dissipation and Dispersion in Nonlinear Partial Differential Equations
Optimal Transport and Stochastic Dynamics
Reaching consensus in heterogeneous random opinion dynamics
ISTplus - Postdoctoral Fellowships
Configuration Spaces over Non-Smooth Spaces
Dissipation and Dispersion in Nonlinear Partial Differential Equations
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; 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.
Publishing Year
Date Published
2024-04-01
Journal Title
Annals of Applied Probability
Publisher
Institute of Mathematical Statistics
Acknowledgement
The first author gratefully acknowledges funding by the Austrian Science Fund (FWF) grant F65, by the European Research Council (ERC, grant agreement No 716117, awarded to Prof. Dr. Jan Maas). He also gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) grant ESPRIT 208.
The second author gratefully acknowledges funding by the Hausdorff Center for Mathematics at the University of Bonn. Part of this work was completed while this author was a member of the Institute of Science and Technology Austria. He gratefully acknowledges funding of his position at that time by the Austrian Science Fund (FWF) grants F65 and W1245.
The third author gratefully acknowledges funding by the Lise Meitner fellowship, Austrian Science Fund (FWF): M3211. Part of this work was completed while funded by the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411.
Volume
34
Issue
2
Page
1789-1845
ISSN
IST-REx-ID
Cite this
Dello Schiavo L, Portinale L, Sau F. Scaling limits of random walks, harmonic profiles, and stationary nonequilibrium states in Lipschitz domains. Annals of Applied Probability. 2024;34(2):1789-1845. doi:10.1214/23-AAP2007
Dello Schiavo, L., Portinale, L., & Sau, F. (2024). Scaling limits of random walks, harmonic profiles, and stationary nonequilibrium states in Lipschitz domains. Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/23-AAP2007
Dello Schiavo, Lorenzo, Lorenzo Portinale, and Federico Sau. “Scaling Limits of Random Walks, Harmonic Profiles, and Stationary Nonequilibrium States in Lipschitz Domains.” Annals of Applied Probability. Institute of Mathematical Statistics, 2024. https://doi.org/10.1214/23-AAP2007.
L. Dello Schiavo, L. Portinale, and F. Sau, “Scaling limits of random walks, harmonic profiles, and stationary nonequilibrium states in Lipschitz domains,” Annals of Applied Probability, vol. 34, no. 2. Institute of Mathematical Statistics, pp. 1789–1845, 2024.
Dello Schiavo L, Portinale L, Sau F. 2024. Scaling limits of random walks, harmonic profiles, and stationary nonequilibrium states in Lipschitz domains. Annals of Applied Probability. 34(2), 1789–1845.
Dello Schiavo, Lorenzo, et al. “Scaling Limits of Random Walks, Harmonic Profiles, and Stationary Nonequilibrium States in Lipschitz Domains.” Annals of Applied Probability, vol. 34, no. 2, Institute of Mathematical Statistics, 2024, pp. 1789–845, doi:10.1214/23-AAP2007.
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