Proof of the Boltzmann-Sinai Ergodic Hypothesis for Typical Hard Disk Systems

Details Proof of the Boltzmann-Sinai Ergodic Hypothesis for Typical Hard Disk Systems Proof of the Boltzmann-Sinai Ergodic Hypothesis for Typical Hard Disk Systems

2000-08-31

arxiv.org/abs/math/0008241v4

Invent. Math. Vol. 154 (2003), No. 1, 123-178

Mathematics

Dynamical Systems

58 pages

Scientific paper

10.1007/s00222-003-0304-9

We consider the system of $N$ ($\ge2$) hard disks of masses $m_1,...,m_N$ and
radius $r$ in the flat unit torus $\Bbb T^2$. We prove the ergodicity
(actually, the B-mixing property) of such systems for almost every selection
$(m_1,...,m_N;r)$ of the outer geometric parameters.

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