Characteristic Functionals of Dirichlet Measures

Abstract

We compute characteristic functionals of Dirichlet-Ferguson measures over a locally compact Polish space and prove continuous dependence of the random measure on the parameter measure. In finite dimension, we identify the dynamical symmetry algebra of the characteristic functional of the Dirichlet distribution with a simple Lie algebra of type $A$. We study the lattice determined by characteristic functionals of categorical Dirichlet posteriors, showing that it has a natural structure of weight Lie algebra module and providing a probabilistic interpretation. A partial generalization to the case of the Dirichlet-Ferguson measure is also obtained.

arXiv comment31 pages, 3 figures

References in corpus (2)

• Means of a Dirichlet process and multiple hypergeometric functions
• Fock factorizations, and decompositions of the $L^2$ spaces over general Levy processes

Cited by in corpus (4)

• The Dirichlet-Ferguson Diffusion on the Space of Probability Measures over a Closed Riemannian Manifold
• A Rademacher-type Theorem on $L^2$-Wasserstein Spaces over Closed Riemannian Manifolds
• A Mecke-type characterization of the Dirichlet-Ferguson measure
• Optimality of universal conclusive entanglement concentration protocols