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Monte Carlo, risk, QMC, statistical efficiency, high dimensional approximation...


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revised closest pair in N-Dimensional
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suggested suggested edit on closest pair in N-Dimensional
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comment closest pair in N-Dimensional
Beware that 2D or 3D shouldnt change much! Sparsity just means a low expected number of points in the slab (of course one could construct "pathologic" or particular counterexamples anyway), so that the algorithm complexity will be low in practice on random input (that is on average, not in the worst case). If you have few points in the slab (say of the order of $d \cdot \sqrt[D/(D-1)]{N})$, then also finding the closest pair will be fast.
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answered closest pair in N-Dimensional
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answered Showing a moving average is strictly stationary if underlying sequence is strictly stationary.