Comments (1)
I believe you're in discussion about this with Hector, but I'll submit this anyway.
As currently stated, Equation 2.2 disagrees with the simulation approach use in the preceding paragraph. Namely, this notation implies that we are choosing two points,
The way you approached your simulation seems to imply computing a different quantity: namely, fix the number of points we are interested in, and then compute the average pairwise distances between all of the points. The expectation of this value will be more complicated to compute analytically (I haven't tried yet), but it seems to be closer to the result you obtained by simulation.
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