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Connect-The-Dots: How many random points can a regular curve pass through?
Curve/Filament Detection. ε-Entropy Confi guration Functions
2015/8/21
Suppose n points are scattered uniformly at random in the unit square [0,1]2. Question:
How many of these points can possibly lie on some curve of length λ? Answer, proved here:
OP (λ ·
√n).