2006/05/25 by Herbert Spohn, Spohn, Herbert · 1 citation
Engineering · Mathematics · Physics and Astronomy · #70F10 #Dynamics and Control of Mechanical Systems #FOS: Physical sciences #Material Science and Thermodynamics #Mathematical Physics (math-ph) #Structural Analysis of Composite Materials #math-ph #math.MP #msc:70F10
paper · pdf · doi:10.48550/arxiv.math-ph/0605068
arxiv created 2006/05/25 · openalex publication_date 2006/05/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In my book ``Large Scale Dynamics of Interacting Particles'' [S] I refer to an unpublished note from early 1985 on the BBGKY hierarchy for hard spheres. My main point there was to provide a direct probabilistic proof for the time-integrated version of the hierarchy. Over recent years there has been repeated interest in this derivation, which encourages me to make my note public. I decided to leave it in its original form including likely inaccuracies. The work of R. Illner and M. Pulvirenti [IP] appeared in September 1985, see also the book by C. Cercignani, R. Illner, and M. Pulvirenti [CIP], who prove the same result using special flow representation and methods from the theory of differential operators. [S] H. Spohn, Large Scale Dynamics of Interacting Particles, Texts and Monographs in Physics, Springer-Verlag, Heidelberg, 1991. [IP] R. Illner and M. Pulvirenti, A derivation of the BBGKY-hierarchy for hard sphere particle systems, Transport Theory and Stat. Phys. 16, 997--1012 (1987), preprint DM-388-IR, September 1985. [CIP] C. Cercignani, R. Illner, and M. Pulvirenti, The Mathematical Theory of Dilute Gases, Applied Mathematical Sciences 106, Springer-Verlag, New York, 1994.