Before revision:  Our key result is that under weak assumptions the estimator of the functional concentrates in a L/ root(n) neighborhood of the target with deviations controlled by the Gaussian law , provided L/root(n) 0;
After revision:  Our key result is that under weak assumptions the estimator of the functional concentrates in a L/ \sqrt{n neighborhood of the target with deviations controlled by the Gaussian law , provided L/root(n) 0;