Abstract:
A number of works are considered which are devoted to the description of the dynamics of a system of an infinite number of interacting particles. The operator method of constructing chains of equations of the type of the chain of Bogolyubov equations is considered in detail, and the relation of this method to the method of creation and annihilation operators of the formalism of second quantization is established. A derivation of the Boltzmann equation from a chain of equations corresponding to the system of Kolmogorov–Feller equations is described.
Citation:
V. P. Maslov, S. È. Tariverdiev, “Asymptotics of the Kolmogorov–Feller equation for a system of a large number of particles”, Itogi Nauki i Tekhniki. Ser. Teor. Veroyatn. Mat. Stat. Teor. Kibern., 19, VINITI, Moscow, 1982, 85–125; J. Soviet Math., 23:5 (1983), 2553–2579
\Bibitem{MasTar82}
\by V.~P.~Maslov, S.~\`E.~Tariverdiev
\paper Asymptotics of the Kolmogorov--Feller equation for a system of a large number of particles
\serial Itogi Nauki i Tekhniki. Ser. Teor. Veroyatn. Mat. Stat. Teor. Kibern.
\yr 1982
\vol 19
\pages 85--125
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intv50}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=657958}
\zmath{https://zbmath.org/?q=an:0517.60100}
\transl
\jour J. Soviet Math.
\yr 1983
\vol 23
\issue 5
\pages 2553--2579
\crossref{https://doi.org/10.1007/BF01084704}
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