Steinhaus's geometric location problem for random samples in the plane
Dorit S. Hochbaum, John M. Steele · Advances in Applied Probability · 1982
Let where X i , 1 ≦ i ≦ n , are i.i.d. and uniformly distributed in [0, 1] 2 . It is proved that M n ∽ cn 1–p/2 a.s. for 1 ≦ p <2. This result is motivated by recent developments in the theory of algorithms and the theory of subadditive processes as well as by a well-known problem of H. Steinhaus.