Let U
1,U
2,… be a sequence of i.i.d. random vectors distributed uniformly in a compact plane region A of unit area. Sufficient conditions on the geometry of A are provided under which the Euclidean diameter D
n
of the first n of the points converges weakly upon suitable rescaling.
Let U1,U2,… be a sequence of i.i.d. random vectors distributed uniformly in a compact plane region A of unit area. Sufficient conditions on the geometry of A are provided under which the Euclidean diameter Dn of the first n of the points converges weakly upon suitable rescaling.
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