Let X, ., X, be independent random vectors that are all uniformly distributed in the circle of
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Let X, ., X, be independent random vectors that are all uniformly distributed in the circle of radius 1 centered at the origin Let T =
T(X,, X,) denote the length of the shortest path connecting these n points. Argue that P{T E[T] a} 2 exp{-a/(32n)}.
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