Related papers: Statistics of Peaks in Chi-Squared Fields
We propose a new approach for the study of the quadratic stochastic Euclidean bipartite matching problem between two sets of $N$ points each, $N\gg 1$. The points are supposed independently randomly generated on a domain…
We re-examine the CHSH experiment, which we abstract here as a multi-round game played between two parties with each party reporting a single binary outcome at each round. We explore in particular the role that symmetries, and the…
The twisted Gaussian Schell Model describes a family of partially coherent beams that present several interesting characteristics, and as such have attracted attention in classical and quantum optics. Recent techniques have been…
We present a general scheme for treating particle beams as many particle systems. This includes the full counting statistics and the requirements of Bose/Fermi symmetry. In the stationary limit, i.e., for longer and longer beams, the total…
A notorious problem in mathematics and physics is to create a solvable model for random sequential adsorption of non-overlapping congruent spheres in the $d$-dimensional Euclidean space with $d\geq 2$. Spheres arrive sequentially at…
Applying the standard weighted mean formula, [sum_i {n_i sigma^{-2}_i}] / [sum_i {sigma^{-2}_i}], to determine the weighted mean of data, n_i, drawn from a Poisson distribution, will, on average, underestimate the true mean by ~1 for all…
We study random spherical harmonics at shrinking scales. We compare the mass assigned to a small spherical cap with its area, and find the smallest possible scale at which, with high probability, the discrepancy between them is small…
A pseudorandom point in an ergodic dynamical system over a computable metric space is a point which is computable but its dynamics has the same statistical behavior as a typical point of the system. It was proved in [Avigad et al. 2010,…
The spectral statistics in the strongly chaotic cardioid billiard are studied. The analysis is based on the first 11000 quantal energy levels for odd and even symmetry respectively. It is found that the level-spacing distribution is in good…
Random field models are mathematical structures used in the study of stochastic complex systems. In this paper, we compute the shape operator of Gaussian random field manifolds using the first and second fundamental forms (Fisher…
We present a novel procedure where a stationary point process is regularized through the convolution with a continuous random field with stationary increments, in the sense that the dependency between distant points is weakened; and the…
The problem of maximizing the average cross section through a point within a shape is introduced. This idea is extended into arbitrary dimensions. However, the average cross sectional volume cannot be maximized unless the cross sections…
We consider the signed density of the extremal points of (two-dimensional) scalar fields with a Gaussian distribution. We assign a positive unit charge to the maxima and minima of the function and a negative one to its saddles. At first, we…
We calculate the average number of critical points of a Gaussian field on a high-dimensional space as a function of their energy and their index. Our results give a complete picture of the organization of critical points and are of…
We numerically investigate the distribution of extrema of 'chaotic' Laplacian eigenfunctions on two-dimensional manifolds. Our contribution is two-fold: (a) we count extrema on grid graphs with a small number of randomly added edges and…
Multiparametric statistical model providing stable reconstruction of parameters by observations is considered. The only general method of this kind is the root model based on the representation of the probability density as a squared…
The first part of this paper extends the Doplicher-Haag-Roberts theory of superselection sectors to quantum field theory on arbitrary globally hyperbolic spacetimes. The statistics of a superselection sector may be defined as in flat…
We investigate the sample paths regularity of operator scaling alpha-stable random fields. Such fields were introduced as anisotropic generalizations of self-similar fields and satisfy a scaling property for a real matrix E. In the case of…
A thorough discussion of the statistical ensemble of scale-free connected random tree graphs is presented. Methods borrowed from field theory are used to define the ensemble and to study analytically its properties. The ensemble is…
The asymptotic distribution of the likelihood-ratio statistic for testing parameters on the boundary is well known to be a chi-squared mixture. The mixture weights have been shown to correspond to the intrinsic volumes of an associated…