The simple exclusion process is one of the most prominent models of interacting particle systems. In this seminar, we consider a resistor network whose nodes are sampled according to a simple point process on R^d and are connected by certain conductances. On top of this resistor network, particles move according to random walks with the rule that there is at most one particle per site.
Under soft assumptions on the point process measure and conductances, which include ergodicity, stationarity and certain moment conditions, it is known that the empirical density of particles converges for almost all realisation of the environment to the solution of an heat equation with a certain homogenised diffusivity.
In this talk, we examine its equilibrium fluctuations. For d≥3, under the same assumptions that ensure the hydrodynamical limit, we show that the empirical density fluctuation field converges for almost all realisation of the environment, in the sense of finite-dimensional distributions, to a generalised Ornstein-Uhlenbeck process. For d=2, if we require some additional regularity on the environment to have Hölder regularity estimates for solutions to parabolic problems, we can show that the same conclusion holds.

See HERE for the full abstract.

TBA