We present a full picture of the out of equilibrium joint fluctuations for current and occupation time in the symmetric exclusion process in dimension one. The main tools developed for that are a Kipnis-Varadhan type inequality necessary to handle the occupation time and a multiple point space time correlation estimate necessary to prove the tightness for the current. Curiously, as a corollary we obtain that, in equilibrium, current and occupation time are independent for any time (but they are not independent seen as processes).

Talk based on a joint work with D. Erhard (UFBA) and T. Xu (UFBA).