Related papers: On the correlation between nodal and boundary leng…
Distance covariance and distance correlation are scalar coefficients that characterize independence of random vectors in arbitrary dimension. Properties, extensions, and applications of distance correlation have been discussed in the recent…
In this paper, we derive nonasymptotic theoretical bounds for the influence in random graphs that depend on the spectral radius of a particular matrix, called the Hazard matrix. We also show that these results are generic and valid for a…
Numerical solutions are given for a parabolic approximation of the acoustic wave equation at 200 and 250 Hz in two and three spatial dimensions to determine if azimuthal coupling in the cross-range coordinate significantly affects…
We consider the correlation structure of the random coefficients for a wide class of wavelet systems on the sphere (Mexican needlets) which were recently introduced in the literature by Geller and Mayeli (2007). We provide necessary and…
Mesoscopic correlations are observed in the polarization of microwave radiation transmitted through a random waveguide. These measurements, supported by diagrammatic theory, permit the unambiguous identification of short, long, and infinite…
We analyze the differences between the horizontal and the vertical component of the simple random walk on the 2-dimensional comb. In particular we evaluate by combinatorial methods the asymptotic behaviour of the expected value of the…
In this paper we prove that as N goes to infinity, the scaling limit of the correlation between critical points z1 and z2 of random holomorphic sections of the N-th power of a positive line bundle over a compact Riemann surface tends to…
Experiments and numerical data on the correlation length for large S disagree strongly with the theoretical prediction based on the effective field theory prescription of the magnon physics. The reason is that for large S, at any accessible…
A navigation on a set of points $S$ is a rule for choosing which point to move to from the present point in order to progress toward a specified target. We study some navigations in the plane where $S$ is a non uniform Poisson point process…
Data uniformity is a concept associated with several semantic data characteristics such as lack of features, correlation and sample bias. This article introduces a novel measure to assess data uniformity and detect uniform pointsets on…
We study the motion of charged Brownian particles in an external magnetic field. It is found that a correlation appears between the components of particle velocity in the case of anisotropic friction, approaching asymptotically zero in the…
We first consider {\it deterministic} immersions of the $d$-dimensional sphere into high dimensional Euclidean spaces, where the immersion is via spherical harmonics of level $n$. The main result of the article is the, a priori unexpected,…
We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the…
We prove the -- to the best knowledge of the authors -- first result on the fine asymptotic behavior of the regular part of the free boundary of the obstacle problem close to singularities. The result is motivated by our recent partial…
The main result presented here is that the flow associated with a riemannian metric and a non zero magnetic field on a compact oriented surface without boundary, under assumptions of hyperbolic type, cannot have the same length spectrum of…
In this paper we consider the convex hull of a spherically symmetric sample in $R^d$. Our main contributions are some new asymptotic results for the expectation of the number of vertices, number of facets, area and the volume of the convex…
We investigate the number of nodal intersections of random Gaussian Laplace eigenfunctions on the standard three-dimensional flat torus with a fixed smooth reference curve, which has nowhere vanishing curvature. The expected intersection…
The statistics of records in sequences of independent, identically distributed random variables is a classic subject of study. One of the earliest results concerns the stochastic independence of record events. Recently, records statistics…
We extend a recent theory of parametric correlations in the spectrum of random matrices to study the response to an external perturbation of eigenvalues near the soft edge of the support. We demonstrate by explicit non-perturbative…
We prove that the length spectrum metric and the arc-length spectrum metric are almost-isometric on the $\epsilon_0$-relative part of Teichmuller spaces of surfaces with boundary.