Related papers: Angle between two random segments
In random sequential covering, identical objects are deposited randomly, irreversibly, and sequentially; only attempts increasing the coverage are accepted. A finite system eventually gets congested, and we study the statistics of congested…
For a spatial characteristic, there exist commonly fat-tail frequency distributions of fragment-size and -mass of glass, areas enclosed by city roads, and pore size/volume in random packings. In order to give a new analytical approach for…
In this work we study a class of random convex sets that "interpolate" between polytopes and zonotopes. These sets arise from considering a $q^{th}$-moment ($q\geq 1$) of an average of order statistics of $1$-dimensional marginals of a…
Among several things, we find the side density for random triangles circumscribing the unit circle and calculate that its median is 5.5482.... An analogous exact computation for perimeter density remains open.
Random packing of unoriented regular polygons and star polygons on a two-dimensional flat, continuous surface is studied numerically using random sequential adsorption algorithm. Obtained results are analyzed to determine saturated random…
What is the probability that a random triangle is acute? We explore this old question from a modern viewpoint, taking into account linear algebra, shape theory, numerical analysis, random matrix theory, the Hopf fibration, and much much…
The distribution function of a random distance in three dimensions is given and some new three-dimensional d2-tests of randomness are suggested. We show that our test statistics are not correlated with the usual test statistics and are…
In this paper, we study the order of the largest connected component of a random graph having two sources of randomness: first, the graph is chosen randomly from all graphs with a given degree sequence, and then bond percolation is applied.…
Random geometric networks consist of 1) a set of nodes embedded randomly in a bounded domain $\mathcal{V} \subseteq \mathbb{R}^d$ and 2) links formed probabilistically according to a function of mutual Euclidean separation. We quantify how…
We study the statistical properties of large random networks with specified degree distributions. New techniques are presented for analyzing the structure of social networks. Specifically, we address the question of how many nodes exist at…
Stochastic simulations are used to characterize the knotting distributions of random ring polymers confined in spheres of various radii. The approach is based on the use of multiple Markov chains and reweighting techniques, combined with…
Computer simulation was used to study the random sequential adsorption of identical discorectangles onto a continuous plane . The problem was analyzed for a wide range of discorectangle aspect ratios ($\varepsilon \in [1;100]$). We studied…
We study the systole of a random surface, where by a random surface we mean a surface constructed by randomly gluing together an even number of triangles. We study two types of metrics on these surfaces, the first one coming from using…
Quantum entanglement is one of the core features of quantum theory. While it is typically revealed by measurements along carefully chosen directions, here we review different methods based on so-called random or randomized measurements.…
Organisms and algorithms learn probability distributions from previous observations, either over evolutionary time or on the fly. In the absence of regularities, estimating the underlying distribution from data would require observing each…
The phenomenom of emerging regular spectral features from random interactions is addressed in the context of the interacting boson model. A mean-field analysis links different regions of the parameter space with definite geometric shapes.…
The dynamics of non-spherical rigid particles immersed in an axisymmetric random flow is studied analytically. The motion of the particles is described by Jeffery's equation; the random flow is Gaussian and has short correlation time.The…
Segmental structure is a common pattern in many types of sequences such as phrases in human languages. In this paper, we present a probabilistic model for sequences via their segmentations. The probability of a segmented sequence is…
Given a parametric polynomial curve $\gamma:[a,b]\rightarrow \mathbb{R}^n$, how can we sample a random point $\mathfrak{x}\in \mathrm{im}(\gamma)$ in such a way that it is distributed uniformly with respect to the arc-length? Unfortunately,…
Contact angle hysteresis of droplets will be examined in light of static friction between liquid drop and solid surface. Unlike frictions in solid-solid interfaces, pinning forces at contact points or contact lines would be the cause of…