Related papers: Statistical properties of the gravitational force …
The zeros of complex Gaussian random polynomials, with coefficients such that the density in the underlying complex space is uniform, are known to have the same statistical properties as the zeros of the coherent state representation of…
To complete a previous work, the probability density functions for the errors in the center-of-gravity as positioning algorithm are derived with the usual methods of the cumulative distribution functions. These methods introduce substantial…
We study a stochastic Hamiltonian system of $N$ particles with many particles interacting through a potential whose range is large in comparison with the typical distance between neighbouring particles. It is shown that the empirical…
We study freely evolving and forced inelastic gases using the Boltzmann equation. We consider uniform collision rates and obtain analytical results valid for arbitrary spatial dimension d and arbitrary dissipation coefficient epsilon. In…
We study the non-stationary Feller process with time varying coefficients. We obtain the exact probability distribution exemplified by its characteristic function and cumulants. In some particular cases we exactly invert the distribution…
In this paper we analyze the influence of transport mechanisms (diffusion and sedimentation) on the structure of monolayers of particles irreversibly adsorbed on a line. We focus our attention on the dependence of the radial distribution…
The lognormal distribution describing, e.g., exponentials of Gaussian random variables is one of the most common statistical distributions in physics. It can exhibit features of broad distributions that imply qualitative departure from the…
This paper is devoted to a statistical analysis of the fluctuations of velocity and acceleration produced by a random distribution of point vortices in two-dimensional turbulence. We show that the velocity probability density function…
It is shown that time reversibility of Hamiltonian microscopic dynamics and Gibbs canonical statistical ensemble of initial conditions for it together produce an exact virial expansion for probability distribution of path of molecular…
Following S\"odergren, we consider a collection of random variables on the space $X_n$ of unimodular lattices in dimension $n$: Normalizations of the angles between the $N = N(n)$ shortest vectors in a random unimodular lattice, and the…
We analyze the structure of stochastic dynamics near either a stable or unstable fixed point, where force can be approximated by linearization. We find that a cost function that determines a Boltzmann-like stationary distribution can always…
Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…
We study the development of gravitational instability in the strongly non-linear regime. For this purpose we use a number of statistical indicators such as filamentary statistics, spectrum of overdense/underdense regions and the void…
Ranking distributions according to a stochastic order has wide applications in diverse areas. Although stochastic dominance has received much attention, convex order, particularly in general dimensions, has yet to be investigated from a…
For a given homogeneous Poisson point process in $\mathbb{R}^d$ two points are connected by an edge if their distance is bounded by a prescribed distance parameter. The behaviour of the resulting random graph, the Gilbert graph or random…
The probability distribution for vacuum fluctuations of the energy flux in two dimensions will be constructed, along with the joint distribution of energy flux and energy density. Our approach will be based on previous work on probability…
The physical property of mass has two distinct aspects, gravitational mass and inertial mass. The weight of a particle depends on its gravitational mass. According to the weak form of the equivalence principle, the gravitational and…
We introduce a sharpness functional for probabilistic models that quantifies sharpness as an intrinsic property of the probability distribution. The measure is derived based on a rank-based concentration principle that tracks upward…
We derive some physical properties of ideal assemblies of identical particles obeying generalized exclusion statistics. We discuss fluctuations, and in this connection point out a fundamental contrast to conventional quantum statistics. We…
The velocity fluctuations for point vortex models are studied for the {\alpha}-turbulence equations, which are characterized by a fractional Laplacian relation between active scalar and the streamfunction. In particular, we focus on the…