Related papers: The distribution function of the distance between …
We propose the first return time distribution (FRTD) of a random walk as an interpretable and mathematically grounded node embedding. The FRTD assigns a probability mass function to each node, allowing us to define a distance between any…
The main result of this paper is a semi-analytic approximation for the chord distribution functions of three-dimensional models of microstructure derived from Gaussian random fields. In the simplest case the chord functions are equivalent…
Theoretical investigations into the deflection angle caused by microlenses offer a direct path to uncovering principles of the cosmological microlensing effect. This work specifically concentrates on the the probability density function…
We consider nanonodes randomly distributed in a circular area and characterize the received signal strength when a pair of these nodes employ molecular communication. Two communication methods are investigated, namely free diffusion and…
This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the $n$ partitions of the interval $[0,W_n]$ are independent and identically distributed…
A wide range of physical problems can be described by randomly-oriented linear trajectories, including any system of objects, organisms, particles, or rays that follow a linear path. Dependent upon the particular random variables that…
We establish a relationship between the two important central lines of the triangle, the Euler line and the Brocard axis, in a configuration with an arbitrary rectangle and a random point. The classical Cartesian coordinate system method…
We prove existence of the large deviation principle, with a proper convex rate function, for the distribution of the renormalized distance from the origin of a random walk on a free product of finitely generated groups. As a consequence, we…
We calculate the distribution with respect to the vacuum state of the distance-$k$ graph of a $d$-regular tree. From this result we show that the distance-$k$ graph of a $d$-regular graphs converges to the distribution of the distance-$k$…
We explore a generating function trick which allows us to keep track of infinitely many statistics using finitely many variables, by recording their individual distributions rather than their joint distributions. Building on previous work…
We analyze a class of continuous time random walks in $\mathbb R^d,d\geq 2,$ with uniformly distributed directions. The steps performed by these processes are distributed according to a generalized Dirichlet law. Given the number of changes…
The triangle distribution function f^(3) for three mutual nearest neighbors in the plane describes basic aspects of short-range order and statistical thermodynamics in two-dimensional many-particle systems. This paper examines prospects for…
We show different expressions of distribution functions (DFs) which depend only on the two classical integrals of the energy and the magnitude of the angular momentum with respect to the axis of symmetry for stellar systems with known…
This paper studies the asymptotic behaviors of the pairwise angles among n randomly and uniformly distributed unit vectors in R^p as the number of points n -> infinity, while the dimension p is either fixed or growing with n. For both…
Random graphs with a given degree sequence are often constructed using the configuration model, which yields a random multigraph. We may adjust this multigraph by a sequence of switchings, eventually yielding a simple graph. We show that,…
We want to approximate general multivariate probability density functions by deterministic sample sets. For optimal sampling, the closeness to the given continuous density has to be assessed. This is a difficult challenge in multivariate…
The characteristic function of the folded normal distribution and its moment function are derived. The entropy of the folded normal distribution and the Kullback--Leibler from the normal and half normal distributions are approximated using…
Randomness is viewed through an analogy between a physical quantity, density of gas, and a mathematical construct -- probability density. Boltzmann's deduction of equilibrium distribution of ideal gas placed in an external potential field…
We investigate the statistical distribution of Newtonian gravitational forces acting on a test particle embedded in an infinite, homogeneous, and uncorrelated random gas of point masses. Using order statistics, we derive the probability…
This paper presents a new method to obtain the distance distribution between the mobile node and any reference node in a regular hexagon. The existing distance distribution research mainly focuses on static network deployment and ignores…