# Proof of the Ergodic Hypothesis for Typical Hard Ball Systems

## Authors

Open AccessArticle

DOI: 10.1007/s00023-004-0166-8

## Abstract.

We consider the system of
\( N (\geq 2) \)
hard balls with masses
\( m_{1}, \ldots, m_{N} \)
and radius *r* in the flat torus
\( \mathbb{T}_{L}^{\nu} = \mathbb{R}^{\nu} / L \cdot \mathbb{Z}^{\nu} \)
of size
\( L, \nu \geq 3 \)
. We prove the ergodicity (actually, the Bernoulli mixing property) of such systems for almost
every selection
\( (m_{1}, \ldots, m_{N}; L) \)
of the outer geometric parameters. This theorem complements my earlier result that proved the same, almost sure ergodicity for the
case
\( \nu = 2 \)
. The method of that proof was primarily dynamical-geometric, whereas
the present approach is inherently algebraic.