A limit theorem for quadratic fluctuations in symmetric simple exclusion

We consider quadratic fluctuations in the centered symmetric simple exclusion process in dimension d=1. Although the order of divergence of is known to be [epsilon]-3/2 if [epsilon][downwards arrow]0, the corresponding limit theorem was so far not explored. We now show that converges in law to a non-Gaussian singular functional of an infinite-dimensional Ornstein-Uhlenbeck process. Despite the singularity of the limiting functional we find enough structure to conclude that it is continuous but not a martingale in t. We remark that in symmetric exclusion in dimensions d>=3 the corresponding functional central limit theorem is known to produce Gaussian martingales in t. The case d=2 remains open.