Hi All , does anybody know an upper bound for the probability of the largest Voronoi cell? More precisely, let x_1 ... x_n be drawn randomly and independently according to a distribution P on R^d. I'm looking for an upper bound of E ( max_{i=1..n} P(B_i) ) where B_i is the Voronoi cell containing x_i, i.e. B_i={x: x_i is the nearest neighbour of x among x_1,...,x_n} I guess this should be O(1/n) ... but not sure. thanks, Daniil