Note (July 21, 2016):
Unfortunately, the main result of this paper was retracted.
For details, see Revision 1 of ECCC TR16-106.
This work addresses one of the two questions regarding two-source extractors that was left open by the breakthrough work of Eshan Chattopadhyay and David Zuckerman: Obtaining negligible error probability, where obtaining long output by addressed by Li. The current work achieves improved error bounds, but only for higher levels of min-entropy.
The current work combines ideas from the recent line of works (including the notion of correlation breakers, see Cohen's consolidation) with Bourgain's earlier ideas.
Warning: The perspective on prior works offered by the current write-up seems lacking.
See ECCC TR16-106.