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May 23, 2015 at 7:50 comment added ofer zeitouni The answer above was expanded (after significant effort) to a full answer for the limsup (including constants) and a partial answer for the liminf. See the joint paper with Elliot Paquette: arxiv.org/abs/1505.05627
Oct 15, 2013 at 15:49 history bounty ended Gil Kalai
Oct 13, 2013 at 16:41 vote accept Gil Kalai
Sep 24, 2013 at 13:40 history edited ofer zeitouni CC BY-SA 3.0
The original answer was completly wrong in scale. The editted post reflects a corrested (log, not loglog) scale
Sep 23, 2013 at 21:14 comment added ofer zeitouni Unfortunately, my answer contains a comedy of calculation mistakes. In the upper bound, one cannot use $a_n=(1+\epsilon)^n$ as I suggested, without an extra argument. If one takes $a_n=n^{3/2}$, which is what the monotonicity allows, one has to replace in the upper bound $\log\log n$ by $\log n$. I will try to update the comment later with details.
Sep 18, 2013 at 3:39 comment added Gil Kalai Many thanks, Ofer!! But where are these doors located?
Sep 17, 2013 at 14:53 history answered ofer zeitouni CC BY-SA 3.0