Related papers: Gaussian integrals on symmetric spaces (the comple…

In symmetric spaces of rank one we obtain a right inverse of the Cartan differential on exact differential forms as an integral operator. As a corollary we extend Gauss linking integral beyond space forms.

We consider Gaussian distributions on certain Riemannian symmetric spaces. In contrast to the Euclidean case, it is challenging to compute the normalization factors of such distributions, which we refer to as partition functions. In some…

Gaussian random matrix ensembles defined over the tangent spaces of the large families of Cartan's symmetric spaces are considered. Such ensembles play a central role in mesoscopic physics since they describe the universal ergodic limit of…

Gaussian distributions can be generalized from Euclidean space to a wide class of Riemannian manifolds. Gaussian distributions on manifolds are harder to make use of in applications since the normalisation factors, which we will refer to as…

We provide a new approach, along with extensions, to results in two important papers of Worsley, Siegmund and coworkers closely tied to the statistical analysis of fMRI (functional magnetic resonance imaging) brain data. These papers…

In this article, we explore a series of elementary yet insightful results involving integrals related to Gaussian sums. Using techniques rooted in classical calculus, we derive several identities and evaluate nontrivial definite integrals…

We construct harmonic Riemannian submersions that are retractions from symmetric spaces of noncompact type onto their rank-one totally geodesic subspaces. Among the consequences, we prove the existence of a non-constant, globally defined…

Complex analysis is a powerful tool to study classical integrable systems, statistical physics on the random lattice, random matrix theory, topological string theory,... All these topics share certain relations, called "loop equations" or…

Recently much effort has been made towards the introduction of non-Hermitian random matrix models respecting $PT$-symmetry. Here we show that there is a one-to-one correspondence between complex $PT$-symmetric matrices and split-complex and…

Heisenberg-type higher order symmetries are studied for both classical and quantum mechanical systems separable in cartesian coordinates. A few particular cases of this type of superintegrable systems were already considered in the…

We study the $G$-strand equations that are extensions of the classical chiral model of particle physics in the particular setting of broken symmetries described by symmetric spaces. These equations are simple field theory models whose…

Riemannian and pseudo-Riemannian symmetric spaces with semisimple transvection group are known and classified for a long time. Contrary to that the description of pseudo-Riemannian symmetric spaces with non-semisimple transvection group is…

The Riemannian geometry of covariance matrices has been essential to several successful applications, in computer vision, biomedical signal and image processing, and radar data processing. For these applications, an important ongoing…

For real hyperbolic spaces, the dynamics of individual isometries and the geometry of the limit set of nonelementary discrete isometry groups have been studied in great detail. Most of the results were generalised to discrete isometry…

Imposing additional constraints on low-rank optimization has garnered growing interest. However, the geometry of coupled constraints hampers the well-developed low-rank structure and makes the problem intricate. To this end, we propose a…

Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…

We show that each classical pseudoriemann symmetric space G/H can be realized as space of pairs of complementary subspaces in a linear space. For each classical symmetric space we construct an open embedding to a grassmannian or to a…

This paper expands the analysis of randomized low-rank approximation beyond the Gaussian distribution to four classes of random matrices: (1) independent sub-Gaussian entries, (2) independent sub-Gaussian columns, (3) independent bounded…

Attention has been brought to the possibility that statistical fluctuation properties of several complex spectra, or, well-known number sequences may display strong signatures that the Hamiltonian yielding them as eigenvalues is…

We consider geometric numerical integration algorithms for differential equations evolving on symmetric spaces. The integrators are constructed from canonical operations on the symmetric space, its Lie triple system (LTS), and the…