  We study the statistics of wave functions in a ballistic chaotic system. The
statistical ensemble is generated by adding weak smooth disorder. The
conjecture of Gaussian fluctuations of wave functions put forward by Berry and
generalized by Hortikar and Srednicki is proven to hold on sufficiently short
distances, while it is found to be strongly violated on larger scales. This
also resolves the conflict between the above conjecture and the wave function
normalization. The method is further used to study ballistic correlations of
wave functions in a random magnetic field.
