  We continue discussion of hard-ball models of statistical mechanics, by
example of random walk of hard ball immersed into equlibrium ideal gas. Our
goal is to highlight decisive role of specific phase-space subsets, despite
their vanishingly smaall Lebesgue measures under the Boltzmann-Grad limit. The
"art of draining" such subsets in conventional mathematical constructions
resulted in loss of so principal property of many-particle systems as 1/f-noise
in diffusivities, mobilities and other transport and relaxation rates. We
suggest new approaches to formulation and analysis of evolution equations for
hierarchy of probability distribution functions of infinite hard-ball systems,
thus further overcoming prejudices of Boltzmannian kinetics and mistakes of its
modern adepts
