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Dec 21, 2018 at 5:14 comment added Anthony Quas Interesting question. I would expect that the depth is approximately normal with mean a multiple of $\log n$ and variance also a multiple of $\log n$. I would expect to be able to compute these constants based on the assumption that the depth is distributed this way, but I have not been able to do so yet.
Dec 20, 2018 at 21:32 comment added Tom Solberg Thanks Mark! Corrected. I would have appreciated an explanation for the downvote as well.
Dec 20, 2018 at 21:32 history edited Tom Solberg CC BY-SA 4.0
Corrected $\ell-X$ per Mark Widon
Dec 20, 2018 at 21:31 comment added Mark Wildon Maybe the downvoter could explain? It looks like there is a typo $X - \ell$ for $\ell - X$, but otherwise it seems like a sensible and maybe interesting question to me.
Dec 20, 2018 at 20:59 history asked Tom Solberg CC BY-SA 4.0