Abstract
The Liouville operator for an infinite-particle Hamiltonian dynamics corresponding to interaction potentialU is used to introduce the concept of a locally weakly invariant measure on the phase space and to show that if a Gibbs measure with potential of general form is locally weakly invariant then its Hamiltonian is asymptotically an additive integral of the motion of the particles with the interactionU.
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References
B. M. Gurevich and V. I. Oseledets, in:Reviews of Science and Technology. Theory of Probability, Mathematical Statistics, and Theoretical Cybernetics, Vol. 14 [in Russian], All-Union Institute of Scientific and Technical Information (VINITI), Moscow (1991), p. 5.
B. M. Gurevich,Usp. Mat. Nauk,41, 193 (1986).
B. M. Gurevich,Tr. MMO,52, 175 (1989).
B. M. Gurevich,Usp. Mat. Nauk,44, 231 (1990).
B. M. Gurevich and Yu. M. Sukhov,Dokl. Akad. Nauk SSSR,223, 276 (1975).
B. M. Gurevich and Ju. M. Suhov,Commun. Math. Phys.,49, 63 (1976).
W. Feller,An Introduction to Probability Theory and its Applications, Vol. 1, Wiley, New York (1950).
Additional information
Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 90, No. 3, pp. 424–459, March, 1992.
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Gurevich, B.M. Gibbs random fields invariant under infinite-particle Hamiltonian dinamics. Theor Math Phys 90, 289–312 (1992). https://doi.org/10.1007/BF01036535
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DOI: https://doi.org/10.1007/BF01036535