Related papers: Correlations between Maxwell's multipoles for gaus…

We compute the generating function of random planar quadrangulations with three marked vertices at prescribed pairwise distances. In the scaling limit of large quadrangulations, this discrete three-point function converges to a simple…

We provide a method for fast and exact simulation of Gaussian random fields on spheres having isotropic covariance functions. The method proposed is then extended to Gaussian random fields defined over spheres cross time and having…

Many star bodies have convex subsets with approximately the same Gaussian measure (of the complement). Inspired by this phenomenon, and in connection with the randomized Dvoretzky theorem for Lorentz spaces, we derive bounds on the…

We investigate the equivalence of Sobolev inequalities and the conjunction of Gaussian upper heat kernel bounds and volume doubling on large scales on graphs. For the normalizing measure, we obtain their equivalence up to constants by…

Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the…

Any homogeneous polynomial $P(x, y, z)$ of degree $d$, being restricted to a unit sphere $S^2$, admits essentially a unique representation of the form $\lambda_0 + \sum_{k = 1}^d \lambda_k [\prod_{j = 1}^k L_{kj}]$, where $L_{kj}$'s are…

Using an integral definition to calculate the relativistic multipole moments (RMM), and the ensuing generalized relativistic Gauss theorem, we prove that the evaluation of that volume integral in Erez-Rosen coordinates, leads to a specific…

Usual Gaussian beams are particular scalar solutions to the paraxial Helmholtz equation, which neglect the vector nature of light. In order to overcome this inconvenience, Simon et al. (J. Opt. Soc. Am. A 1986, 3, 536-540) found a paraxial…

The covariant formulation of Maxwell's equations can be expressed in a form independent of the usual systems of units by introducing the constants alpha, beta and gamma into these equations. Maxwell's equations involving these constants are…

Cosmological correlators encode statistical properties of the initial conditions of our universe. Mathematically, they can often be written as Mellin integrals of a certain rational function associated to graphs, namely the flat space…

We relate the distribution of eigenvalues of a random symmetric matrix in the Gaussian Orthogonal Ensemble to the distribution of critical values of a random linear combination of eigenfunctions of the Laplacian on a compact Riemann…

Two-dimensional Maxwell-dilaton quantum gravity, which covers a large family of the actions for two-dimensional gravity (in particular, string-inspired models) is investigated. Charged black holes which appear in the theory are briefly…

An exact solution is given for a two-dimensional model of a Coulomb gas, more general than the previously solved ones. The system is made of a uniformly charged background, positive particles, and negative particles, on the surface of a…

We investigate how the shape of the galaxy two-point correlation function as measured in the zCOSMOS survey depends on local environment, quantified in terms of the density contrast on scales of 5 Mpc/h. We show that the flat shape…

This paper studies the one-loop expansion of the amplitudes of electromagnetism about flat Euclidean backgrounds bounded by a 3-sphere, recently considered in perturbative quantum cosmology, by using zeta-function regularization. For a…

Wavefunction correlations and density matrices for few or many particles are derived from the properties of semiclassical energy Green functions. Universal features of fixed energy (microcanonical) random wavefunction correlation functions…

Using an estimate on the number of critical points for a Morse-even function on the sphere $\mathbb S^m$, $m\ge1$, we prove a multiplicity result for orthogonal geodesic chords in Riemannian manifolds with boundary that are diffeomorphic to…

The Maxwell operator in a 3D cylinder is considered. The coefficients are assumed to be scalar functions depending on the longitudinal variable only. Such operator is represented as a sum of countable set of matrix differential operators of…

In these notes, we describe the recent progress in understanding the zero sets of two remarkable Gaussian random functions: the Gaussian entire function with invariant distribution of zeroes with respect to isometries of the complex plane,…

Peculiar velocities encode rich cosmological information, but their transverse components are hard to measure. Here, we present the first observations of a novel effect of transverse velocities: the dipole signatures that they imprint on…