Kondratiev Yu. G.
Ukr. Mat. Zh. - 2005. - 57, № 5. - pp. 3-11
Infinite systems of stochastic differential equations and some lattice models on compact Riemannian manifolds
Ukr. Mat. Zh. - 1997. - 49, № 3. - pp. 326–337
Stochastic dynamics associated with Gibbs measures on an infinite product of compact Riemannian manifolds is constructed. The probabilistic representations for the corresponding Feller semigroups are obtained. The uniqueness of the dynamics is proved.
Ukr. Mat. Zh. - 1993. - 45, № 4. - pp. 451–458
Periodic Gibbs states for quantum lattice systems are investigated. We formulate the definition of the periodic Gibbs states and the measures associated with them. Theorems of existence are proved for these states. We also prove the existence of the critical temperature for the system of anharmonic quantum oscillators with pairwise interaction.
Ukr. Mat. Zh. - 1983. - 35, № 6. - pp. 753–756
Ukr. Mat. Zh. - 1976. - 28, № 1. - pp. 27–35