Related papers: Wiener distribution on holonomy groups

We prove convergence of symmetric diffusions on Wiener spaces by using stopping times arguments and capacity techniques. The drifts of the diffusions can be singular, we require the densities of the processes to be neither bounded from…

We prove a mean ergodic theorem for amenable discrete quantum groups. As an application, we prove a Wiener type theorem for continuous measures on compact metrizable groups.

In the paper, we give the proof of the polar decomposition of the Wiener measure according to the orbits of the group of diffeomorphisms.

We deal with random processes obtained from a homogeneous random process with independent increments by replacement of the time scale and by multiplication by a norming constant. We prove the convergence in distribution of these processes…

We prove the following monotonicity result for the holonomy group: Given a sequence of metric connections converging in $C^0$ such that all its members have holonomy contained in a closed group $H$, also their limit connection needs to have…

This paper uses a net-theoretic approach to convergence spaces, aimed to simplify the description of continuous convergence in order to apply it in problems concerning Homotopy Theory. We present methods for handling homotopies of limit…

We prove a genuine analogue of Wiener Tauberian theorem for hypergeometric transforms. As an application we prove analogue of Furstenberg theorem on Harmonic functions.

We prove quantitative polynomial Wiener-Wintner theorems in a very general setup, including measure-preserving actions of nilpotent Lie groups. Our results apply both to ergodic averages and to averages with singular integral weights. The…

This work explores new classes of nonstationary stochastic sequences associated with polynomial hypergroups. Their covariance structures are analyzed through positive definite kernels and corresponding Hilbert spaces. Novel consistent…

In this paper we consider permutations of sequences of partitions, obtaining a result which parallels von Neumann's theorem on permutations of dense sequences and uniformly distributed sequences of points.

Some parts of stochastic analysis on curved spaces are revisted. A concise proof of the quasi-invariance of the Wiener measure on the path spaces over a Riemannian manifold is presented. The shifts are allowed to be in the Cameron-Martin…

We prove a Berger-type theorem which asserts that if the orthogonal subgroup generated by the torsion tensor (pulled back to a point by parallel transport) of a metric connection with skew-symmetric torsion is not transitive on the sphere,…

In this paper we extend the homogenization results obtained in (G. Allaire, A. Mikeli\'c, A. Piatnitski, J. Math. Phys. 51 (2010), 123103) for a system of partial differential equations describing the transport of a N-component electrolyte…

This paper is motivated by recent developments of higher gauge theory. Different from its style of using higher category theory, we try to describe the concept of higher parallel transport within setting of classical principal bundle…

A measure on a locally compact group is called spread out if one of its convolution powers is not singular with respect to Haar measure. Using Markov chain theory, we conduct a detailed analysis of random walks on homogeneous spaces with…

We introduce horizontal holonomy groups, which are groups defined using parallel transport only along curves tangent to a given subbundle $D$ of the tangent bundle. We provide explicit means of computing these holonomy groups by deriving…

We prove the following nonholonomic version of the classical Moser theorem: given a bracket-generating distribution on a connected compact manifold (possibly with boundary), two volume forms of equal total volume can be isotoped by the flow…

Inspired by an extension of Wiener's lemma on the relation of measures $\mu$ on the unit circle and their Fourier coefficients $\widehat{\mu}(k_n)$ along subsequences $(k_n)$ of the natural numbers by Cuny, Eisner and Farkas [CEF19,…

In this paper we prove a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds.

In this paper we propose a method to construct probability measures on the space of convex bodies with a given pushforward distribution. Concretely we show that there is a measure on the metric space of centrally symmetric convex bodies,…