I am interested in knowing which is the expected length of a random path in a circle. That is, if there are $n$ random points located in the unitary circle $\{(x,y): x^2+y^2\leq 1\}$, what is the expected length of the shortest path the connects all of them starting from the origin? In Wikipedia there are some results regarding the unitary square, but I have found nothing for the unitary circle. Thanks!
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$\begingroup$ you mean the unit disc rather than the unit circle, don't you? $\endgroup$– Carlo BeenakkerCommented Sep 20, 2021 at 13:54
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$\begingroup$ Do you know the Beardwood-Halton-Hammersley-theorem? $\endgroup$– Jochen WengenrothCommented Sep 20, 2021 at 16:13
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$\begingroup$ That theorem answers my question, thanks! $\endgroup$– user105059Commented Sep 21, 2021 at 14:32
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