  We study the generation of CMB anisotropies by gravitational lensing on small
angular scales. We show these fluctuations are not Gaussian. We prove that the
power spectrum of the tail of the CMB anisotropies on small angular scales
directly gives the power spectrum of the deflection angle. We show that the
generated power on small scales is correlated with the large scale gradient.
The cross correlation between large scale gradient and small scale power can be
used to test the hypothesis that the extra power is indeed generated by
lensing. We compute the three and four point function of the temperature in the
small angle limit. We relate the non-Gaussian aspects presented in this paper
as well as those in our previous studies of the lensing effects on large scales
to the three and four point functions. We interpret the statistics proposed in
terms of different configurations of the four point function and show how they
relate to the statistic that maximizes the S/N.
