  We compute the fluctuations of the number of bosons with a given momentum for
the Tonks-Girardeau gas at zero temperature. We show that correlations between
opposite momenta, which is an important fingerprint of long range order in
weakly interacting Bose systems, are suppressed and that the full distribution
of the number of bosons with non zero momentum is exponential. The distribution
of the quasi-condensate is however quasi Gaussian. Experimental relevance of
our findings for recent cold atoms experiments are discussed.
