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Proof of the Boltzmann-Sinai ergodic hypothesis for typical hard disk systems

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Abstract

We consider the system of N (≥2) hard disks of masses m 1,...,m N and radius r in the flat unit torus 𝕋2. 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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Authors and Affiliations

  1. Department of Mathematics, University of Alabama at Birmingham, Campbell Hall, 35294, Birmingham, AL, USA

    Nándor Simányi

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  1. Nándor Simányi
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Correspondence to Nándor Simányi.

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Dedicated to Ya. G. Sinai honoring his 65th birthday

Mathematics Subject Classification (2000)

37D50, 34D05

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Simányi, N. Proof of the Boltzmann-Sinai ergodic hypothesis for typical hard disk systems. Invent. math. 154, 123–178 (2003). https://doi.org/10.1007/s00222-003-0304-9

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  • DOI: https://doi.org/10.1007/s00222-003-0304-9

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