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Aug 21, 2012 at 17:20 comment added TerronaBell Yeah, I think we're on the same page -- allowing more time to pass is equivalent to putting larger weights on larger values of $k$. So if the weights decay slowly then the central limit theorem will take over. (And if they decay quickly, it won't!)
Aug 21, 2012 at 0:43 history answered Will Sawin CC BY-SA 3.0