相关论文: Spatial statistics for lattice points on the spher…

A family of generalized binomial probability distributions attached to Landau levels on the Riemann sphere is introduced by constructing a kind of generalized coherent states. Their main statistical parameters are obtained explicitly. As…

Let $U_1,\ldots,U_n$ be independent random vectors uniformly distributed on the unit sphere $\mathbb S^{d-1}\subseteq\mathbb R^d$, where $n\ge d$, and consider the random polyhedral cone \[ \mathcal W_{n,d}:=\mathop{\mathrm{pos}}…

Here I will review the theoretical results that have been obtained for spin glasses. I will concentrate my attention on the predictions of the mean field approach in three dimensional systems and on its numerical and experimental…

For sampling values along spherical Lissajous curves we establish a spectral interpolation and quadrature scheme on the sphere. We provide a mathematical analysis of spherical Lissajous curves and study the characteristic properties of…

We analyze the scattering dynamics and spectrum of a quantum particle on a tight-binding lattice subject to a non-Hermitian (purely imaginary) local potential. The reflection, transmission and absorption coefficients are studied as a…

This paper presents a unified theory for the power of a point with respect to generalized spheres (spheres, horospheres, and hyperspheres) in $n$-dimensional hyperbolic space $\mathbf{H}^n$. By extending the classical secant theorem, we…

We study the formation of images in a reflective sphere in three configurations using caustics of the field of light rays. The optical wavefront emerging from a source point reaching a subject following passage through the optical system…

The spherical orthogonal, unitary, and symplectic ensembles (SOE/SUE/SSE) $S_\beta(N,r)$ consist of $N \times N$ real symmetric, complex hermitian, and quaternionic self-adjoint matrices of Frobenius norm $r$, made into a probability space…

A spherical distribution is an eigendistribution of the Laplace-Beltrami operator with certain invariance on the de Sitter space. Let G'=O(1,n;R) be the Lorentz group and H' = O(1,n-1;R) be its subgroup. The authors Olafsson and Sitiraju…

Statistical lattice ensembles of loops in three or more dimensions typically have phases in which the longest loops fill a finite fraction of the system. In such phases it is natural to ask about the distribution of loop lengths. We show…

We examine SERS from two perspectives: as a phenomenon described by the Laplace Equation (the electrostatic or Rayleigh limit) and by the Helmholtz Equation (electrodynamic or Mie limit). We formulate the problem in terms of the scalar…

Two-point functions of the scalar curvature for metric fluctuations on the four-sphere are analysed. The two-point function for points separated by a fixed distance and for metrics of fixed volume is calculated using spacetime foam methods.…

A circle, centered at the origin and with radius chosen so that it has non-empty intersection with the integer lattice $\mathbb{Z}^{2}$, gives rise to a probability measure on the unit circle in a natural way. Such measures, and their weak…

The concept of typical and weighted typical spherical faces for tessellations of the $d$-dimensional unit sphere, generated by $n$ independent random great hyperspheres distributed according to a non-degenerate directional distribution, is…

In some applications, like some areas in stochastic geometry, a convenient change of variables involves spheres. In this review we summarize formulas of Blaschke-Petkantschin type, that help to pass from integration over $k$-tuples of…

The main purpose of these lectures is to discuss briefly recent methods of calculation of statistical properties of quantum eigenvalues for chaotic systems based on semi-classical trace formulas. Under the assumption that periodic orbit…

We consider a percolation model on square lattices with sites weighted by beta-distributed random variables $S\sim \mathrm{Beta}(a,b)$ with a positive real parameters $a>0$ and $b>0$. Using the Monte Carlo method, we estimate the…

We analyze the statistical properties of bubble models for the large-scale distribution of galaxies. To this aim, we realize static simulations, in which galaxies are mostly randomly arranged in the regions surrounding bubbles. As a first…

We consider a local average in the hyperbolic lattice point counting problem for the Picard group $\Gamma$ acting on the three-dimensional hyperbolic space. Compared to the pointwise case, we improve the bounds on the remainder in the…

We give the cumulative distribution functions, the expected values, and the moments of weighted lattice polynomials when regarded as real functions of independent random variables. Since weighted lattice polynomial functions include…