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The physical properties of a classical many-particle system with interactions given by a repulsive Gaussian pair potential are extended to arbitrarily high Euclidean dimensions. The goals of this paper are to characterize the behavior of…
We construct a family of measures for random fields based on the iterated subdivision of simple geometric shapes (triangles, squares, tetrahedrons) into a finite number of similar shapes. The intent is to construct continuum limits of scale…
I discuss the impact of gauge-gravity duality on our understanding of two classes of systems: conformal quantum matter and compressible quantum matter. The first conformal class includes systems, such as the boson Hubbard model in two…
We introduce and study covariance fields of distributions on a Riemannian manifold. At each point on the manifold, covariance is defined to be a symmetric and positive definite (2,0)-tensor. Its product with the metric tensor specifies a…
Gauss-Bonnet holographic fluid is a useful theoretical laboratory to study the effects of curvature-squared terms in the dual gravity action on transport coefficients, quasinormal spectra and the analytic structure of thermal correlators at…
A decoupling type inequality for a sum of functions of Guassian vectors is established.
In this note, we study two-point correlation functions of modular Hamiltonians. We show that in general quantum systems, these correlators obey properties similar to those of von Neumann entropy and capacity of entanglement, both of which…
We consider three-dimensional reshaping of thin nemato-elastic sheets containing half-charged defects upon nematic-isotropic transition. Gaussian curvature, that can be evaluated analytically when the nematic texture is known, differs from…
The two-point correlation function in thin films is studied near the critical point of the corresponding bulk system. Based on fieldtheoretic renormalization group theory the dependences of this correlation function on the lateral momentum,…
Measurements of resonant tunneling through a localized impurity state are used to probe fluctuations in the local density of states of heavily doped GaAs. The measured differential conductance is analyzed in terms of correlation functions…
We developed the functional form of the two-point correlation function under the approximation of fixed particle number density n(bar). We solved the quasi-linear partial differential equation (PDE) through the method of characteristics to…
Applying advances in exact computations of supersymmetric gauge theories, we study the structure of correlation functions in two-dimensional N=(2,2) Abelian and non-Abelian gauge theories. We determine universal relations among correlation…
Geometrical model of structure of the universe is examined to obtain analytical expression for the two points nonlinear correlation function. According to the model the objects (galaxies) are concentrated into two types of structure…
This work aims to extend the existing results on thick points of logarithmic-correlated Gaussian Free Fields to Gaussian random fields that are more singular. To be specific, we adopt a sphere averaging regularization to study…
The Klein-Grifone approach to global Finsler geometry is adopted. The nullity distributions of the three curvature tensors of Cartan connection are investigated. Nullity distributions concerning certain relevant special Finsler spaces are…
Gaussian processes (GPs) are popular nonparametric statistical models for learning unknown functions and quantifying the spatiotemporal uncertainty in data. Recent works have extended GPs to model scalar and vector quantities distributed…
We consider the statistical distribution of zeros of random meromorphic functions whose poles are independent random variables. It is demonstrated that correlation functions of these zeros can be computed analytically and explicit…
The two-point gauge-invariant correlation function of gluonic field strengths, which is the main input in the stochastic vacuum model, is derived by using its relation to the Green functions of one- and two-gluon gluelumps. These Green…
We discuss a numerical analysis employing the density of partition function zeroes which permits effective distinction between phase transitions of first and second order, elucidates crossover between such phase transitions and gives a new…
We study sampling properties of the zero set of the Gaussian entire function on Fock spaces. Firstly, we relax Seip and Wallst\'en's density and separation conditions for sampling sets on Fock spaces to obtain weighted inequalities for sets…