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Dirichlet operators via stochastic analysis. (English) Zbl 0820.60042

Summary: We give sufficient conditions for essential self-adjointness of symmetric differential operators (Dirichlet operators) associated with classical Dirichlet forms given by probability measures on Hilbert spaces. Under an additional assumption of log-concavity for the measures we prove the existence of a gap at the lower end of spectrum of the Dirichlet operator and the ergodicity of the corresponding semigroup. We consider also applications to the study of stochastic dynamics in some classical lattice systems.

MSC:

60H25 Random operators and equations (aspects of stochastic analysis)
35J99 Elliptic equations and elliptic systems
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