Related papers: Random chords and point distances in regular polyg…
In this paper, the statistical properties of Newton s method algorithm output in a specific case have been studied. The relative frequency density of this sample converges to a well-defined function, prompting us to explore its…
We examine numerically the distribution function $f_K(r)$ of distance $r$ between opposite polygonal nodes for random polygons of $N$ nodes with a fixed knot type $K$. Here we consider three knots such as $\emptyset$, $3_1$ and $3_1 \sharp…
We consider the distribution of free path lengths, or the distance between consecutive bounces of random particles, in an n-dimensional rectangular box. If each particle travels a distance R, then, as R tends to infinity the free path…
Parallelograms are one of the basic building blocks in two-dimensional tiling. They have important applications in a wide variety of science and engineering fields, such as wireless communication networks, urban transportation, operations…
This paper continues description of applications of signed chord length distribution started in part I (arXiv:0711.4734). It is shown simple relation between equation for some transfer integrals with source and target bodies and different…
Motivated by models in engineering and also biology we determine in closed form the probability density function of the angle shaped by two random chords in a fixed disc. Our main result focus on the event in which the intersection locates…
In wireless networks, the knowledge of nodal distances is essential for several areas such as system configuration, performance analysis and protocol design. In order to evaluate distance distributions in random networks, the underlying…
Analytical expressions for the distribution of the length of chords corresponding to the affine invariant measure on the set of chords are given for convex polygons. These analytical expressions are a computational improvement over other…
Where are the intersection points of diagonals of a regular $n$-gon located? What is the distribution of the intersection point of two random chords of a circle? We investigate these and related new questions in geometric probability,…
We present a method to characterize the distribution of length-scales of finite, disordered patterns with, on average, radial symmetry. This method makes it possible to quantify the distribution of characteristic length scales in cases…
When we represent a network of sensors in Euclidean space by a graph, there are two distances between any two nodes that we may consider. One of them is the Euclidean distance. The other is the distance between the two nodes in the graph,…
For the given regular plane polygon and an arbitrary point in the plane of the polygon, the distances from the point to the vertices of the polygon are defined. We proved that there is one more non-congruent regular polygon having the…
Let $K\subset\mathbb S^{d-1}$ be a convex spherical body. Denote by $\Delta(K)$ the distance between two random points in $K$ and denote by $\sigma(K)$ the length of a random chord of $K$. We explicitly express the distribution of…
We first review the derivation of the exact expression for the average distance $<r_n>$ of the n-th neighbour of a reference point among a set of N random points distributed uniformly in a unit volume of a D-dimensional geometric space.…
The Dirac's chord method may be suitable in different areas of physics for the representation of certain six-dimensional integrals for a convex body using the probability density of the chord length distribution. For a homogeneous model…
We provide a robust and general algorithm for computing distribution functions associated to induced orthogonal polynomial measures. We leverage several tools for orthogonal polynomials to provide a spectrally-accurate method for a broad…
This paper extends earlier work on the distribution in the complex plane of the roots of random polynomials. In this paper, the random polynomials are generalized to random finite sums of given "basis" functions. The basis functions are…
We review some probabilistic properties of the sum-of-digits function of random integers. New asymptotic approximations to the total variation distance and its refinements are also derived. Four different approaches are used: a classical…
Although previous research has found several facts concerning chord lengths of regular polytopes, none of these investigations has considered whether any of these facts define relationships that might generalize to the chord lengths of all…
We study the moments and the distribution of the discrete Choquet integral when regarded as a real function of a random sample drawn from a continuous distribution. Since the discrete Choquet integral includes weighted arithmetic means,…