Fluctuations des temps d’occupation d’un site dans l’exclusion simple symétrique. (Fluctuations in the occupation time of a site in simple symmetric exclusion). (French) Zbl 0612.60094

Kipnis, C.

Ann. Inst. Henri Poincaré, Probab. Stat. 23, 21-35 (1987).

It is proved that in the simple symmetric exclusion process the fluctuations of the occupation time of a site, properly renormalized, converge to a normal random variable. The normalizing function turns out to be the same as in the case without interaction. The proof is based on a central limit theorem for martingales.

Reviewer: M.Mürmann

MSC:

60K35	Interacting random processes; statistical mechanics type models; percolation theory
60F05	Central limit and other weak theorems

Keywords:

infinite particle system; simple symmetric exclusion process; fluctuations of the occupation time; central limit theorem for martingales