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Stochastic Analysis on (Infinite-Dimensional) Product Manifolds

In: Stochastic Dynamics

Author

Listed:
  • Sergio Albeverio
  • Alexei Daletskii
  • Yuri Kondratiev

Abstract

We give a review of our results related to stochastic analysis on product manifolds (infinite products of compact Riemannian manifolds). We introduce differentiable structures on product manifolds and prove the existence and uniqueness theorem for stochastic differential equations on them. This result is applied to the construction of Glauber dynamics for classical lattice models with compact spin spaces. We discuss the relations between ergodicity of the dynamics and extremality of the corresponding Gibbs measures. Further, we construct the associated stochastic dynamics in the space of macroscopic fluctuations of our system.

Suggested Citation

  • Sergio Albeverio & Alexei Daletskii & Yuri Kondratiev, 1999. "Stochastic Analysis on (Infinite-Dimensional) Product Manifolds," Springer Books, in: Stochastic Dynamics, chapter 15, pages 339-369, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-22655-2_15
    DOI: 10.1007/0-387-22655-9_15
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