We shall upper bound :

Then, Taylor expand the logarithm, and asymptotically only the first two terms contribute. If you do this out, you should get the bound .

This weakens the resulting bound by a constant factor of , but the exponential term will turn out to be the same. This is of course assuming I didn't make any stupid mistakes (I really hope!). Overall a great article though–fantastic exposition and blog post. I really learned a lot, thanks!

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