Related papers: Some properties of rectangle and a random point
We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…
As an example of the concept of rulial space, we explore the case of simple Turing machines. We construct the rulial multiway graph which represents the behavior of all possible Turing machines with a certain class of rules. This graph…
We study the Carnot theorem and the configuration of points and lines in connection with it. It is proven that certain significant points in the configuration lie on the same lines and same conics. The proof of an equivalent statement…
Inspired by the recent results toward Birkhoff conjecture (a rigidity property of billiards in ellipses), we discuss two rigidity properties of conics. The first one concerns symmetries of an analog of polar duality associated with an oval,…
It is shown that the point charge and magnetic moment of electron produce together such a field that total electromagnetic momentum has a component perpendicular to electron velocity. As a result classical electron models, having magnetic…
Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean Random Matrices in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different…
Random graphs have proven to be one of the most important and fruitful concepts in modern Combinatorics and Theoretical Computer Science. Besides being a fascinating study subject for their own sake, they serve as essential instruments in…
In many situations, the statistical properties of wave systems with chaotic classical limits are well-described by random matrix theory. However, applications of random matrix theory to scattering problems require introduction of system…
We construct random triangles via uniform sampling of certain families of lines in the plane. Two examples are given. The word "uniform" turns out to be vague; two competing models are examined. Everything we write is well-known to experts.…
The paper concerns lattice triangulations, that is, triangulations of the integer points in a polygon in $\mathbb{R}^2$ whose vertices are also integer points. Lattice triangulations have been studied extensively both as geometric objects…
Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…
We study a large class of Bernoulli percolation models on random lattices of the half- plane, obtained as local limits of uniform planar triangulations or quadrangulations. We first compute the exact value of the site percolation threshold…
Random tensor models can be used as combinatorial devices to generate Euclidean dynamical triangulations. A physical continuum limit of dynamical triangulations requires a suitable generalization of the double-scaling limit of random…
The authors have discussed the method and merit of introducing the curvilinear coordinates into numerical analysis and have shown some numerical examples. However, they used analytical functions for the mappings in the examples and didn't…
Random key graphs are random graphs induced by the random key predistribution scheme of Eschenauer and Gligor under the assumption of full visibility. For this class of random graphs we show the existence of a zero-one law for the…
We interpret a normal surface in a (singular) three-manifold in terms of the homology of a chain complex. This allows us to study the relation between normal surfaces and their quadrilateral co-ordinates. Specifically, we give a proof of an…
We investigate connections between the geometry of linear subspaces and the convergence of the alternating projection method for linear projections. The aim of this article is twofold: in the first part, we show that even in Euclidean…
The observed strong dark-to-luminous matter coupling is described by a bias relation between visible and dark matter sources. We discuss the bias which emerges in the case where the topological structure of the Universe at very large…
We consider the geometry of random interlacements on the $d$-dimensional lattice. We use ideas from stochastic dimension theory developed in \cite{benjamini2004geometry} to prove the following: Given that two vertices $x,y$ belong to the…
The curse of dimensionality is a common phenomenon which affects analysis of datasets characterized by large numbers of variables associated with each point. Problematic scenarios of this type frequently arise in classification algorithms…