  It is shown that time reversibility of Hamiltonian microscopic dynamics and
Gibbs canonical statistical ensemble of initial conditions for it together
produce an exact virial expansion for probability distribution of path of
molecular Brownian particle in a fluid. This expansion leads to inequality
connecting logarithmic derivative of the distribution with respect to fluid
density and characteristic volume occupied by pair statistical correlation
between the path and fluid molecules. Due to the inequality, finiteness of this
volume means that asymptotic of the distribution is essentially non-Gaussian.
For principal case when fluid is dilute gas it is demonstrated that the pair
correlation volume is actually finite and bounded above. Therefore even under
the Boltzmann-Grad limit the path distribution possess power-law long tails
(cut off at distances of ballistic flight).
