Equilibrium fluctuations for the slow boundary exclusion process

TL;DR

This paper characterizes the equilibrium fluctuations of the symmetric simple exclusion process with slow boundaries, showing they converge to an Ornstein-Uhlenbeck process with boundary conditions determined by the boundary slowness parameter.

Contribution

It establishes the limiting fluctuation process for the exclusion process with slow boundaries, connecting boundary slowness to specific boundary conditions in the limiting process.

Findings

Fluctuations converge to an Ornstein-Uhlenbeck process.

Boundary conditions depend on the slowness parameter.

Results unify different boundary behaviors under a common framework.

Abstract

We prove that the equilibrium fluctuations of the symmetric simple exclusion process in contact with slow boundaries is given by an Ornstein-Uhlenbeck process with Dirichlet, Robin or Neumann boundary conditions depending on the range of the parameter that rules the slowness of the boundaries.