On the relationships between some approaches to the solution of Kirkwood-Salsburg equations. (English. Ukrainian original) Zbl 1489.82020
Ukr. Math. J. 73, No. 3, 447-462 (2021); translation from Ukr. Mat. Zh. 73, No. 3, 381-394 (2021).
Summary: We propose a brief survey devoted to the description of the solutions of Kirkwood-Salsburg equations for correlation functions in the grand canonical ensemble. We establish analytic relationships between the Ruelle operator approach described in detail in [D. Ruelle, Statistical mechanics. Rigorous results. New York-Amsterdam: W. A. Benjamin, Inc. (1969; Zbl 0177.57301)] and the approach developed by R. A. Minlos and S. K. Pogosyan in [“Estimates of Ursell functions, group functions, and their derivatives” (Russian), Teor. Mat. Fiz. 31, No. 2, 199–213 (1977)]. Based on the methods of infinite-dimensional analysis, we propose a more transparent description of the main results.
MSC:
| 82B21 | Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics |
| 82C22 | Interacting particle systems in time-dependent statistical mechanics |
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
| 45H05 | Integral equations with miscellaneous special kernels |
Citations:
Zbl 0177.57301References:
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