A limit theorem for particle current in the symmetric exclusion process. (English) Zbl 1226.60138

Vandenberg-Rodes, Alexander

Electron. Commun. Probab. 15, 240-252 (2010).

Summary: Using the recently discovered strong negative dependence properties of the symmetric exclusion process, we derive general conditions for when the normalized current of particles between regions converges to the Gaussian distribution. The main novelty is that the results do not assume any translation invariance, and hold for most initial configurations.

MSC:

60K35

Interacting random processes; statistical mechanics type models; percolation theory

Keywords:

symmetric exclusion process; stability; particle current; central limit theorem