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10 votes
1 answer
484 views

Stochastic Covering Number of a Convex Set

Consider a convex set, say S=[0,1]d. Let X1,X2,,Xn, be i.i.d. random variables that are uniformly distributed on S. Denote the Euclidean ball centered at xRd ...
6 votes
1 answer
330 views

Best and worst centrally symmetric convex covering shapes

Suppose you have a centrally symmetric convex 2D shape C of area A, and you randomly throw down copies of C on the plane so that each C-center lies within a given unit square S, until S is ...