Kakeya Sets, New Mergers and Old Extractors

A merger is a probabilistic procedure which extracts therandomness out of any (arbitrarily correlated) set of randomvariables, as long as one of them is uniform. Our main result isan efficient, simple, optimal (to constant factors) merger, which,for $k$ random vairables on $n$ bits each, uses a $O(\log(nk))$seed, and whose error is $1/nk$. Our merger can be viewed as aderandomized version of the merger of Lu, Reingold, Vadhan andWigderson (2003). Its analysis