Asymptotic behavior of density in the boundary-driven exclusion process on the Sierpinski gasket

Abstract

We derive the macroscopic laws that govern the evolution of the density of particles in the exclusion process on the Sierpinski gasket in the presence of a variable speed boundary. We obtain, at the hydrodynamics level, the heat equation evolving on the Sierpinski gasket with either Dirichlet or Neumann boundary conditions, depending on whether the reservoirs are fast or slow. For a particular strength of the boundary dynamics we obtain linear Robin boundary conditions. As for the fluctuations, we prove that, when starting from the stationary measure, namely the product Bernoulli measure in the equilibrium setting, they are governed by Ornstein-Uhlenbeck processes with the respective boundary conditions.

45 pages, 2 figures. Final version, to appear in Math. Phys. Anal. Geom

References in corpus (8)

• Exclusion process with slow boundary
• Stationary and Nonequilibrium Fluctuations in Boundary Driven Exclusion Processes
• Slow to fast infinitely extended reservoirs for the symmetric exclusion process with long jumps
• Hydrodynamic limit for a zero-range process in the Sierpinski gasket
• The moving particle lemma for the exclusion process on a weighted graph
• Hydrodynamic limit of the Symmetric Exclusion Process on a compact Riemannian manifold
• Asymptotic behavior of density in the boundary-driven exclusion process on the Sierpinski gasket
• Equilibrium fluctuations for the Symmetric Exclusion Process on a compact Riemannian manifold

Cited by in corpus (3)

• Higher order hydrodynamics and equilibrium fluctuations of interacting particle systems
• Asymptotic behavior of density in the boundary-driven exclusion process on the Sierpinski gasket
• The cutoff profile for exclusion processes in any dimension