Related papers: Random K\"ahler Metrics
We review how a reduction procedure along a principal fibration and an unfolding procedure associated to a suitable momentum map allow to describe the K\"ahler geometry of a finite dimensional complex projective spaces.
We introduce slant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds as a generalization of slant immersions, invariant Riemannian maps and anti-invariant Riemannian maps. We give examples, obtain characterizations and…
This paper explores methods for estimating or approximating the total variation distance and the chi-squared divergence of probability measures within topological sample spaces, using independent and identically distributed samples. Our…
This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…
We study the manifold of all Riemannian metrics over a closed, finite-dimensional manifold. In particular, we investigate the topology on the manifold of metrics induced by the distance function of the L^2 Riemannian metric - so called…
Motivated by the problem of nonparametric inference in high level digital image analysis, we introduce a general extrinsic approach for data analysis on Hilbert manifolds with a focus on means of probability distributions on such sample…
Quantum area tensor Regge calculus is considered, some properties are discussed. The path integral quantisation is defined for the usual length-based Regge calculus considered as a particular case (a kind of a state) of the area tensor…
A simple method of obtaining path-integral measures in higher-derivative gravities is presented. The measures are nothing but the generalized Lee-Yang terms.
In Bayesian theory, calculating a posterior probability distribution is highly important but usually difficult. Therefore, some methods have been put forward to deal with such problem, among which, the most popular one is the asymptotic…
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…
The aim of this paper is to present some properties of Choquet maximal Radon probability measures on compact, convex subsets of Hausdorff, locally convex, topological real vector spaces. Theorem 3.12 is the main result of the paper. While…
We give a partial account of some problems concerning cohomological invariants and metric properties of complex non-K\"ahler manifolds.
On a smooth connected manifold, we consider all possible locally elliptic and locally bounded measurable coefficient Riemannian metrics called rough Riemannian metrics. We equip this set with an extended metric which is connected if and…
The purpose of this paper is to prove the finiteness theorems for meromorphic mappings of a complete connected K\"{a}hler manifold into projective space sharing few hyperplanes in subgeneral position without counting multiplicity, where all…
We show how to perform integrals over products of distributions in coordinate space such as to reproduce the results of momentum space Feynman integrals in dimensional regularization. This ensures the invariance of path integrals under…
This report presents a new, algorithmic approach to the distributions of the distance between two points distributed uniformly at random in various polygons, based on the extended Kinematic Measure (KM) from integral geometry. We first…
This article discusses the problem of estimation of parameters in finite mixtures when the mixture components are assumed to be symmetric and to come from the same location family. We refer to these mixtures as semi-parametric because no…
The subject of this paper is six-dimensional nearly (para-)K\"ahler geometry with pseudo-Riemannian metrics. Firstly, we derive the analogue of the well-known exterior differential system characterising a nearly K\"ahler manifold and prove…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
This paper describes an algorithm of interest. This is a preliminary version and we intend on writing a better descripition of it and getting bounds for its complexity.