Phase transition in the exclusion process on the Sierpinski gasket with slowed boundary reservoirs

Joe P. Chen, Patrícia Gonçalves

Published 2019-04-18Version 1

We derive the macroscopic laws that govern the evolution of the density of particles in the exclusion process evolving on the Sierpinski gasket in the presence of a slow boundary. Depending on the slowness of the 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 also 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.