Let H. (resp., H ) be a real and separable Hubert space with Borel O'field T (resp., rj, and let (H. X //-, T, X T.) be the product measurable space generated by the measurable rectangles. This paper develops relations between probability measures on (H. x H , V x T.), i.e., joint measures, and the projections of such measures on (H., T.) and (H , Y ). In particular, the class of all joint Gaus...

The cohomology of the BRS operator corresponding to a group of rigid symmetries is studied in a space of local field functionals subjected to a condition of gauge invariance. We propose a procedure based on a filtration operator counting the degree in the infinitesimal parameters of the rigid symmetry transformations. An application to Witten’s topological Yang-Mills theory is given. PACS codes...

We introduce and study covariance fields of distributions on a Riemannian manifold. At each point on the manifold, covariance is defined to be a symmetric and positive definite (2,0)-tensor. Its product with the metric tensor specifies a linear operator on the respected tangent space. Collectively, these operators form a covariance operator field. We show that, in most circumstances, covariance...

The goal of this paper is to establish relative perturbation bounds, tailored for empirical covariance operators. Our main results are expansions eigenvalues and spectral projectors, leading concentration inequalities limit theorems. One the key ingredients a specific separation measure population eigenvalues, which we call rank, giving rise sharp invariance principle in terms theorems, inconsi...