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Nov 2, 2011 at 9:50 vote accept Julien Berestycki
Nov 1, 2011 at 23:29 comment added Louigi Addario-Berry Sorry, you're right. That's what I get for commenting before my first coffee. I've corrected my response. Welcome to MO.
Nov 1, 2011 at 23:28 history edited Louigi Addario-Berry CC BY-SA 3.0
Corrected some incorrect math.
Nov 1, 2011 at 16:40 comment added Julien Berestycki Thanks for pointing me to this! I had in the back of my mind that Aldous had surely considered a version of this problem but didn't think to check his open problem list. By the way, I imagine that $L_n$ is of order $n^{1/2}$ and not $n^{-1/2}$ ($L_n$ can't be smaller than the diameter of the cloud of points and therefore cannot tends to 0). I was also made aware of this work projecteuclid.org/… which seems relevant.
Nov 1, 2011 at 8:09 history answered Louigi Addario-Berry CC BY-SA 3.0