nearest neighbor: Voronoi cells

[Daniil Riabko]

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