Abstract:
This is a survey of the present state of the method of the generating functional which makes it possible to effectively study distributions of point random measures on a complete, separable metric space. The principal attention is devoted to the study of distributions of configurations of infinite systems of statistical physics — Gibbs distributions.
Citation:
G. I. Nazin, “Method of the generating functional”, Itogi Nauki i Tekhniki. Ser. Teor. Veroyatn. Mat. Stat. Teor. Kibern., 22, VINITI, Moscow, 1984, 159–201; J. Soviet Math., 31:2 (1985), 2859–2886
\Bibitem{Naz84}
\by G.~I.~Nazin
\paper Method of the generating functional
\serial Itogi Nauki i Tekhniki. Ser. Teor. Veroyatn. Mat. Stat. Teor. Kibern.
\yr 1984
\vol 22
\pages 159--201
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intv60}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=778386}
\zmath{https://zbmath.org/?q=an:0566.60048|0571.60068}
\transl
\jour J. Soviet Math.
\yr 1985
\vol 31
\issue 2
\pages 2859--2886
\crossref{https://doi.org/10.1007/BF02116603}
Linking options:
https://www.mathnet.ru/eng/intv60
https://www.mathnet.ru/eng/intv/v22/p159
This publication is cited in the following 5 articles:
V. V. Ryazanov, “Obtaining the thermodynamic relations for the Gibbs ensemble using the maximum entropy method”, Theoret. and Math. Phys., 194:3 (2018), 390–403
Yuri Kondratiev, Yuri Kozitsky, “Evolution of states in a continuum migration model”, Anal.Math.Phys., 8:1 (2018), 93
Yuri G. Kondratiev, Tobias Kuna, Maria João Oliveira, “Holomorphic Bogoliubov functionals for interacting particle systems in continuum”, Journal of Functional Analysis, 238:2 (2006), 375
Yu. G. Kondrat'ev, A. M. Chebotarev, “Bernstein theorems and transformations of correlation measures in statistical physics”, Math. Notes, 79:5 (2006), 649–663
G. I. Nazin, A. V. Tatosov, “Solution of Kirkwood–Salsburg equations for a one-dimensional lattice gas”, Theoret. and Math. Phys., 102:3 (1995), 336–340
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