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. - 1995. - 47, № 3. - pp. 299–306
For Gibbs temperature states, the scheme of the proof of the noncommutative central limit theorem is given by using the commutative central limit theorem for corresponding Euclidean measures. Applications are constructed for the model of a temperature-anharmonic crystal and the generalized Ising model with compact continuous configuration space.
Essential self-adjointness of Dirichlet operators of Gibbs measures on infinite products of manifolds
Ukr. Mat. Zh. - 1995. - 47, № 1. - pp. 4–11
We obtain the conditions of essential self-adjointness of Dirichlet operators of Gibbs measures with essential domains consisting of smooth cylindrical functions. It is proved that certain spaces of smooth functions are invariant under the action of the semigroup of the Dirichlet operator.
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