Infinite systems of stochastic differential equations and some lattice models on compact Riemannian manifolds

DOI10.1007/BF02487239zbMath0941.58022WikidataQ115392113 ScholiaQ115392113MaRDI QIDQ4270816

Alexei Daletskii, Sergio A. Albeverio, Yuri G. Kondratiev

Publication date: 22 November 1999

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

stochastic differential equationstochastic dynamicsGibbs measurelattice systemDirichlet operator

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Diffusion processes and stochastic analysis on manifolds (58J65) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)

Related Items (5)

STOCHASTIC EQUATIONS AND QUASI-INVARIANCE ON INFINITE PRODUCT GROUPS ⋮ The Dirichlet-Ferguson diffusion on the space of probability measures over a closed Riemannian manifold ⋮ Sergio's work in statistical mechanics: from quantum particles to geometric stochastic analysis ⋮ Stochastic differential equations on product loop manifolds. ⋮ Stochastic analysis on product manifolds: Dirichlet operators on differential forms

Cites Work

• On solutions to stochastic differential equations with discontinuous drift in Hilbert space
• Diffusions on an infinite dimensional torus
• The logarithmic Sobolev inequality for continuous spin systems on a lattice
• The equivalence of the logarithmic Sobolev inequality and the Dobrushin- Shlosman mixing condition
• Smoothing properties of semigroups for Dirichlet operators of Gibbs measures
• Dirichlet operators via stochastic analysis
• Uniqueness of the stochastic dynamics for continuous spin systems on a lattice
• A stochastic differential equation approach to some lattice models on compact Lie groups
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