Exact bounds for the stochastic upward matching problem

We draw at random independently and according to the uniform distribution two sets of n points of the unit square We consider a maximum matching of points of the first set with points of the second set with the restriction that a point can be matched only with a point located at its upper right. Then with probability close to one, the number of unmatched points is of order nl/2 (log n)3/4 .