Abstract:
This review article deals with mathematical problems related to the time evolution of systems of infinitely many particles. The probabilistic aspect of the obtained results is emphasized.
Citation:
B. M. Gurevich, V. I. Oseledets, “Some mathematical problems related to the nonequilibrium statistical mechanics of infinitely many particles”, Itogi Nauki i Tekhniki. Ser. Teor. Veroyatn. Mat. Stat. Teor. Kibern., 14, VINITI, Moscow, 1977, 5–39; J. Soviet Math., 13:4 (1980), 455–478
\Bibitem{GurOse77}
\by B.~M.~Gurevich, V.~I.~Oseledets
\paper Some mathematical problems related to the nonequilibrium statistical mechanics of infinitely many particles
\serial Itogi Nauki i Tekhniki. Ser. Teor. Veroyatn. Mat. Stat. Teor. Kibern.
\yr 1977
\vol 14
\pages 5--39
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intv31}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=652301}
\zmath{https://zbmath.org/?q=an:0405.60093|0437.60080}
\transl
\jour J. Soviet Math.
\yr 1980
\vol 13
\issue 4
\pages 455--478
\crossref{https://doi.org/10.1007/BF01673627}
Linking options:
https://www.mathnet.ru/eng/intv31
https://www.mathnet.ru/eng/intv/v14/p5
This publication is cited in the following 5 articles:
Kinetic Boltzmann, Vlasov and Related Equations, 2011, 289
B. M. Gurevich, “Gibbs random fields invariant under infinite-particle Hamiltonian dinamics”, Theoret. and Math. Phys., 90:3 (1992), 289–312
V. I. Skripnik, “Evolution operator of the Bogolyubov gradient diffusion hierarchy in the mean field limit”, Theoret. and Math. Phys., 79:1 (1989), 431–436
B. M. Gurevich, “In ariant measures of dynamical systems of statistical mechanics and first integrals of Hamiltonian systems with finitely many degrees of freedom”, Russian Math. Surveys, 41:2 (1986), 201–202
V. P. Belavkin, V. P. Maslov, S. È. Tariverdiev, “Asymptotic dynamics of a system of a large number of particles described by the Kolmogorov–Feller equations”, Theoret. and Math. Phys., 49 (1981), 1043–1049
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