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We present new exact solutions for two-dimensional geometries generated by continuous distributions of topological defects within a conformal metric framework. By reformulating Einstein's equations in two dimensions as a Poisson equation…
The mass density distribution of Newtonian self-gravitating systems is studied analytically in field theoretical method. Modeling the system as a fluid in hydrostatical equilibrium, we apply Schwinger's functional derivative on the average…
Gaussian processes are machine learning models capable of learning unknown functions in a way that represents uncertainty, thereby facilitating construction of optimal decision-making systems. Motivated by a desire to deploy Gaussian…
We report on a high temperature perturbation expansion study of the superfluid-density spatial correlation function of a Ginzburg-Landau-model superconducting film in a magnetic field. We have derived a closed form which expresses the…
We calculate the primordial correlation of gravitons with an abelian gauge field non-minimally coupled through a dynamical dilaton field or a volume moduli during inflation in the early universe. In particular, we compute the…
Gaussian particles provide a flexible framework for modelling and simulating three-dimensional star-shaped random sets. In our framework, the radial function of the particle arises from a kernel smoothing, and is associated with an…
Massive and massless Gaussian free fields can be described as generalized Gaussian processes indexed by an appropriate space of functions. In this article we study various approaches to approximate these fields and look at the fractal…
The dominant theme of this thesis is that random matrix valued analytic functions, generalizing both random matrices and random analytic functions, for many purposes can (and perhaps should) be effectively studied in that level of…
In this paper, we study the geometric nonlinearity properties, such as curvature and torsion, in a dual coordinate system of the Riemannian manifold defined by the Gaussian distribution. We also give the Amari formulas explicitly in this…
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…
The main aim of this paper is twofold. First we generalize, in a novel way, most of the known non-vanishing results for the derivatives of the Riemann zeta function by establishing the existence of an infinite sequence of regions in the…
A random vector whose norm and overlap (inner product with an independent copy) concentrates is shown to have random low-dimensional projections that are approximately random Gaussians. Conversely, asymptotically random Gaussian projections…
Spatially embedded networks are important in several disciplines. The prototypical spatial net- work we assume is the Random Geometric Graph of which many properties are known. Here we present new results for the two-point degree…
The (negative) gradient vector fields of Morse functions on a compact manifold provide an important example in dynamical system. In this note we prove two important properties of this kind of vector field: Connectedness of critical points…
We figure out the explicit expression for the trace of the field equations associated to generic higher derivative theories of gravity endowed with Lagrangians depending upon the metric and its Riemann tensor, together with arbitrary order…
On a spacetime $(M,g)$ endowed with a density function $h$, we consider the vacuum weighted Einstein field equations: \[h\rho-\operatorname{Hes}_h+\Delta h g=0.\] First, it is shown that the equation characterizes critical metrics for an…
The dynamics of the torsion field is analyzed in the framework of the Covariant Canonical Gauge Theory of Gravity (CCGG), a De~Donder-Weyl Hamiltonian formulation of gauge gravity. The action is quadratic in both, the torsion and the…
Many statistics available to constrain non-Gaussianity from inflation are simplest to use under the assumption that the curvature correlation functions are hierarchical. That is, if the n-point function is proportional to the (n-1) power of…
We define bilinear functionals of vector fields and differential forms, the densities of which yield the metric and Einstein tensors on even-dimensional Riemannian manifolds. We generalise these concepts in non-commutative geometry and, in…
Consider randomly picked points inside the n-dimensional unit hypersphere centered at the origin of the Cartesian coordinate system. The Cartesian coordinates of the points are random variables, which form an n-dimensional vector for each…