Stochastic analysis on product manifolds: Dirichlet operators on differential forms
Consider a product manifold \(\mathbf M\), namely an infinite product of identical compact Riemannian manifolds. The aim of this work is to study the differential calculus on \(\mathbf M\), and to deduce a construction of Dirichlet operators on differential forms. More precisely, the analogues of Bochner and de Rham operators are defined. Properties of the corresponding semigroups are obtained by a probabilistic technique, more precisely by considering stochastic differential equations on tensor bundles over \(\mathbf M\). Finally, this study is related to Gibbs measures on \(\mathbf M\).
scientific article; zbMATH DE number 1529986
scientific article