Geometric analysis for symmetric Fleming-Viot operators: Rademacher's theorem and exponential families (Q1611956)

This paper contains a number of very interesting results about symmetric Fleming-Viot operators and their associated Dirichlet forms. Using the natural geometry of a symmetric Fleming-Viot operator \({\mathcal L}\) the author obtains analytical descriptions of the corresponding Dirichlet space \(({\mathcal E}, {\mathcal D}({\mathcal E}))\). In particular, a complete characterization of functions in \({\mathcal D}({\mathcal E})\) in terms of their differentiability properties along exponential families are given. One of the main results is a Rademacher theorem stating that any function which is Lipschitz continuous with respect to the Bhattacharya distance is contained in \({\mathcal D}({\mathcal E})\) and possesses a bounded gradient. A converse to this statement is also given.