Geodesic
On random fields corresponding to the BBGKY, Vlasov, and Boltzmann hierarchies
Teoretičeskaâ i matematičeskaâ fizika, Tome 54 (1983) no. 1, pp. 78-88 Cet article a éte moissonné depuis la source Math-Net.Ru

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A‘correspondence is established between the creation and annihilation operators introduced by Maslov and Tariverdiev [10] for the densities of the Bogolyubov and Boltzmann hierarchies and the transformations of the measures of the random fields associated with the hierarchies. Bogolyubov’s equation in variational derivatives for the moment functional of the hierarchies [1] is replaced by an equation for the characteristic functional, which is an infinite-dimensional Fourier transform of a measure. The measures of the random fields of the hierarchies satisfy infinitedimensional analogs of the known equations. These equations are written down by means of creation and annihilation operators acting on functionals and measures. 
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     title = {On random fields corresponding to {the~BBGKY,} {Vlasov,} and {Boltzmann} hierarchies},
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V. P. Maslov; A. M. Chebotarev. On random fields corresponding to the BBGKY, Vlasov, and Boltzmann hierarchies. Teoretičeskaâ i matematičeskaâ fizika, Tome 54 (1983) no. 1, pp. 78-88. http://geodesic.mathdoc.fr/item/TMF_1983_54_1_a6/

[1] Bogolyubov N. N., Problemy dinamicheskoi teorii v statisticheskoi fizike, GITTL, 1946, 118 pp. | MR

[2] Vladimirov V. S., UMN, 15:4 (1960), 129–135 | MR | Zbl

[3] Vladimirov V. S., Obobschennye funktsii, Nauka, M., 1979, 320 pp. | MR

[4] Danford N., Shvarts Dzh., Lineinye operatory, IL, M., 1962, 895 pp. | MR

[5] Dobrushin R. L., Funkts. analiz i ego pril., 13:2 (1979), 48–58 | MR | Zbl

[6] Klimontovich Yu. L., Statisticheskaya fizika, Nauka, M., 1982, 608 pp. | MR

[7] Maslov V. P., Operatornye metody, Nauka, M., 1973, 544 pp. | MR

[8] Maslov V. P., “Uravneniya samosoglasovannogo polya”, Itogi nauki i tekhniki. Problemy sovremennoi matematiki, 11, VINITI AN SSSR, Moskva, 1978, 153–234 | MR

[9] Maslov V. P., Belavkin V. P., TMF, 33:1 (1977), 17–31 | MR

[10] Maslov V. P., Tariverdiev S. E., “Asimptotika uravneniya Kolmogorova-Fellera dlya sistemy bolshogo chisla chastits”, Itogi nauki i tekhniki. Teor. veroyatn. mat. statistika. teor. kibernetika, 19, VINITI AN SSSR, Moskva, 1982, 85–125 | MR

[11] Chebotarev A. M., DAN SSSR, 225 (1975), 763–766 | MR | Zbl

[12] Batt J., Ann. Nucl. Energy, 7:4–5 (1980), 213–217 | DOI | MR

[13] Braun W., Hepp K., Commun. Math. Phys., 56:2 (1977), 101–113 | DOI | MR | Zbl

[14] Narnhofer H., Sewell G. L., Commun. Math. Phys., 79 (1981), 9–24 | DOI | MR

[15] Spohn H., Math. Meth. in Appl. Sci., 3:4 (1981), 445–455 | DOI | MR | Zbl