Proof of the Ergodic Hypothesis for Typical Hard Ball Systems

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We consider the system of N (≥2) hard balls with masses m₁,...,mₙ and radius r in the flat torus Tₗν= Rν/L· Zν of size L, ν≥3. We prove the ergodicity (actually, the Bernoulli mixing property) of such systems for almost every selection (m₁,...,mₙ; L) of the outer geometric parameters. This theorem complements my earlier result that proved the same, almost sure ergodicity for the case ν=2. The method of that proof was primarily dynamical-geometric, whereas the present approach is inherently algebraic.