相关论文: Geometrical Statistics--Classical and Quantum
We develop a statistical framework for conducting inference on collections of time-varying covariance operators (covariance flows) over a general, possibly infinite dimensional, Hilbert space. We model the intrinsically non-linear structure…
In an attempt to characterize the distribution of forms and shapes of nodal domains in wave functions, we define a geometric parameter - the ratio $\rho$ between the area of a domain and its perimeter, measured in units of the wavelength…
The relevance of the concept of Fisher information is increasing in both statistical physics and quantum computing. From a statistical mechanical standpoint, the application of Fisher information in the kinetic theory of gases is…
Classical mechanical systems are central to controller design in energy shaping methods of geometric control. However, their expressivity is limited by position-only metrics and the intimate link between metric and geometry. Recent work on…
This paper is about Dirichlet averages in the matrix-variate case or averages of functions over the Dirichlet measure in the complex domain. The classical power mean contains the harmonic mean, arithmetic mean and geometric mean (Hardy,…
We consider an inference on the eigenvalues of the covariance matrix of a multivariate normal distribution. The family of multivariate normal distributions with a fixed mean is seen as a Riemannian manifold with Fisher information metric.…
Since Berry's pioneering 1984 work, the separation of geometric and dynamic contributions in the {\it phase} of an evolving wave has become fundamental in physics, underpinning diverse phenomena in quantum mechanics, optics, and condensed…
Probabilistic frames are a generalization of finite frames into the Wasserstein space of probability measures with finite second moment. We introduce new probabilistic definitions of duality, analysis, and synthesis and investigate their…
We explore the positive geometry of statistical models in the setting of toric varieties. Our focus lies on models for discrete data that are parameterized in terms of Cox coordinates. We develop a geometric theory for computations in…
In this paper, we introduce a new generalization of geometric distribution which can also viewed as discrete analogue of weighted exponential distribution introduced by Gupta and Kundu(2009). We study some basic distributional properties…
Several new geometric quantile-based measures for multivariate dispersion, skewness, kurtosis, and spherical asymmetry are defined. These measures differ from existing measures, which use volumes and are easy to calculate. Some theoretical…
We investigate properties of some extensions of a class of Fourier-based probability metrics, originally introduced to study convergence to equilibrium for the solution to the spatially homogeneous Boltzmann equation. At difference with the…
Lie algebraic techniques are powerful and widely-used tools for studying dynamics and metrology in quantum optics. When the Hamiltonian generates a Lie algebra with finite dimension, the unitary evolution can be expressed as a finite…
The Bures metric is a natural choice in measuring the distance of density operators representing states in quantum mechanics. In the past few years a random matrix ensemble and the corresponding joint probability density function of its…
The unavoidable interaction between a quantum system and the external noisy environment can be mimicked by a sequence of stochastic measurements whose outcomes are neglected. Here we investigate how this stochasticity is reflected in the…
Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…
A regularization procedure, that allows one to relate singularities of curvature to those of the Einstein tensor without some of the shortcomings of previous approaches, is proposed. This regularization is obtained by requiring that (i) the…
Our results concern geometry of a manifold endowed with a pair of complementary orthogonal distributions (plane fields) and a time-dependent Riemannian metric. The work begins with formulae concerning deformations of geometric quantities as…
Fisher matrices play an important role in experimental design and in data analysis. Their primary role is to make predictions for the inference of model parameters - both their errors and covariances. In this short review, I outline a…
This article contains a survey of the geometric approach to quantum correlations. We focus mainly on the geometric measures of quantum correlations based on the Bures and quantum Hellinger distances.