A limit theorem for quadratic fluctuations in symmetric simple exclusion

Sigurd Assing

Stochastic Processes and their Applications, 2007, vol. 117, issue 6, 766-790

Abstract: 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.

Keywords: Exclusion; process; Ornstein-Uhlenbeck; process; Scaling; limit; Fluctuation; field; Gaussian; analysis (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (1)

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