Abstract
Stochastic dynamics associated with Gibbs measures on \(M^{Z^d }\), where M is a compact Riemannian manifold and Z d is an integer lattice, is considered. Equivalence of its L 2-ergodicity and the extremality of the corresponding Gibbs measure is proved.
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Albeverio, S., Daletskii, A., Kondratiev, Y., Röckner, M. (2001). Stochastic Dynamics of Compact Spins: Ergodicity and Irreducibility. In: Accardi, L., Kuo, HH., Obata, N., Saito, K., Si, S., Streit, L. (eds) Recent Developments in Infinite-Dimensional Analysis and Quantum Probability. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0842-6_2
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DOI: https://doi.org/10.1007/978-94-010-0842-6_2
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