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The BBGKY hierarchy of equations for a particle interacting with ideal gas isanalyzed in terms of irreducible many-particle correlations between gas atomsand the particle's motion. The transition to the hard-sphere interaction isformulated from viewpoint of the recently discovered exact relations connectingthe correlations with the particle's probability distribution. Then theBoltzmann-Grad limit is considered and shown not to lead to the Bolzmannhierarchy and the molecular chaos, since correlations of all orders keepsignificant.in this limit, merely taking a singular form.

Hard-sphere Brownian motion in ideal gas: inter-particle correlations, Boltzmann-Grad limit, and destroying the myth of molecular chaos propagation