Định lý giới hạn trung tâm cho khí lý tưởng
Tóm tắt
Từ khóa
Tài liệu tham khảo
Dobrushin, R.L.: Perturbation methods of the theory of Gibbsian fields. In: Bernard, P. (ed.) Lectures on Probability Theory and Statistics. LNM, vol. 1648. Springer, Berlin (1996)
Ginibre, J.: Reduced density matrices of quantum gases I. Limit of infinite volume. J. Math. Phys. 6, 238–251 (1965). II. Cluster property. J. Math. Phys. 6, 252–262 (1965), III. Hard-core potentials. J. Math. Phys. 6, 1432–1446 (1965)
Halfina, A.M.: The limiting equivalence of the canonical and grand canonical ensembles (low density case). Math. USSR, Sb. 9, Article ID 1 (1969)
Heinrich, L.: Mixing properties of Gibbsian point processes and asymptotic normality of Takacs–Fiksel estimates, Preprint 92-051, Universität Bielefeld (1992)
Heinrich, L.: On the strong Brillinger-mixing property of α-determinantal point processes and some applications. Appl. Math. 61, 443–461 (2016)
Jensen, J.L., Künsch, H.R.: On asymptotic normality of pseudo likelihood estimates for pairwise interacting processes. Ann. Inst. Statist. Math. 46, 475–486 (1994)
Malyshev, V.A.: The central limit theorem for Gibbsian random fields. Sov. Math., Dokl. 16(5), 1141–1145 (1975)
Malyshev, V.A., Minlos, R.A.: Gibbs Random Fields,. Cluster Expansions. Mathematics and Its Applications (Soviet Series), vol. 44. Kluwer Academic, Dordrecht (1991)
Martin-Löf, A.: Mixing properties, differentiablity of the free energy and the central limit theorem for a pure phase in the Ising model at low temperature. Comm. Math. Phys. 32, 75–92 (1973)
Mecke, J.: Stationäre Maße auf lokalkompakten Abelschen Gruppen. Z. Wahrsch. Verw. Gebiete 9, 36–58 (1967)
Mecke, J.: Random Measures–Classical Lectures. Walter Warmuth Verlag, Nächst Neuendorf (2011)
Minlos, R.A., Halfina, A.M.: Two-dimensional limit theorem for the particle number and energy in the grand canonical ensemble. Math. USSR, Izv. 4, Article ID 5 (1970)
Nehring, B.: Construction of Classical and Quantum Gases. The Method of Cluster Expansions. Walter Warmuth Verlag, Nächst Neuendorf (2013)
Nehring, B.: Construction of point processes for classical and quantum gases. J. Math. Phys. 54, 053304 (2013)
Nguyen, X.X., Zessin, H.: Integral and differential characterizations of the Gibbs process. Math. Nachr. 88, 105–115 (1979)
Poghosyan, S., Ueltschi, D.: Abstract cluster expansion with applications to statistical mechanical systems. J. Math. Phys. 50, 053509 (2009)
Poghosyan, S., Zessin, H.: Cluster representations of classical and quantum processes. Mosc. Math. J. 19(1), 1–19 (2019)
Poghosyan, S., Zessin, H.: Penrose-Stable Interactions in Classical Statistical Mechanics. Annales Henri Poincaré., vol. 23. Springer, Cham (2022)
Ruelle, D.: Statistical Mechanics, Rigorous Results, 3rd edn. Imperial College Press and World Scientific Publishing (1999)
Ueltschi, D.: An improved tree-graph bound. arXiv:1705.05353v1 [math-phys] (15 May 2017)