Related papers: Pins, Stakes, Anchors and Gaussian Triangles

We describe efficient algorithms to search for cases in which binomial coefficients are equal or almost equal, give a conjecturally complete list of all cases where two binomial coefficients differ by 1, and give some identities for…

When studying convergence of measures, an important issue is the choice of probability metric. In this review, we provide a summary and some new results concerning bounds among ten important probability metrics/distances that are used by…

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 formulate a general family of entanglement criteria for multipartite systems. Fisher information criteria compare the sensitivity to unitary rotations with the variances of suitable local observables. Generalized squeezing-type criteria…

We prove a simple criterion of exponential tightness for sequences of Gaussian r.v.'s with values in a separable Banach space from which we deduce a general result of Large Deviations which allows easily to obtain LD estimates in various…

A class of trigonometric interpolation splines depending on parameter vectors, selected convergence factors and interpolation factors is considered. The concept of crosslink grids and interpolation grids is introduced; these grids can match…

Gaussian random fields on finite dimensional smooth manifolds whose variances reach their maximum value at smooth submanifolds are considered. Exact asymptotic behaviors of large excursion probabilities have been evaluated. Vector Gaussian…

In this paper we consider the notions of binomial thinning, binomial mixing, their generalizations, certain interplay between them, associated limit theorems and provide various examples.

Random arrangements of points in the plane, interacting only through a simple hard core exclusion, are considered. An intensity parameter controls the average density of arrangements, in analogy with the Poisson point process. It is proved…

The density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional ingredient to the description of the linear space carrying…

This white paper collects some open questions in several different aspects of axion theories. The questions are related to quantization of axion couplings, axion-magnetic monopole systems, axions in quantum gravity theory, axion…

This survey explores the foundational theory and recent developments in the study of hyperuniformity. We present a comprehensive mathematical framework in the context of weakly stationary random measures, emphasizing spectral…

Gaussian random fields on Euclidean spaces whose variances reach their maximum values at unique points are considered. Exact asymptotic behaviors of probabilities of large absolute maximum of theirs trajectories have been evaluated using…

In this somewhat pedagogical paper we revisit complementarity relations in bipartite quantum systems. Focusing on continuous variable systems, we examine the influential class of EPR-like states through a generalization to Gaussian states…

Stack triangulations appear as natural objects when defining an increasing family of triangulations by successive additions of vertices. We consider two different probability distributions for such objects. We represent, or "draw" these…

We calculate the average number of critical points of a Gaussian field on a high-dimensional space as a function of their energy and their index. Our results give a complete picture of the organization of critical points and are of…

Given independent normally distributed points A,B,C,D in Euclidean 3-space, let Q denote the plane determined by A,B,C and D^ denote the orthogonal projection of D onto Q. The probability that the tetrahedron ABCD is acute remains…

We investigate the uncertainty associated with a joint quantum measurement of two components of spin of a spin-1/2 particle and quantify this in terms of entropy. We consider two entropic quantities: the joint entropy and the sum of the…

Using a recently developed method to simulate percolation on large clusters of distributed machines [N. R. Moloney and G. Pruessner, Phys. Rev. E 67, 037701 (2003)], we have numerically calculated crossing, spanning and wrapping…

We extend our recent study of winding number density statistics in Gaussian random matrix ensembles of the chiral unitary (AIII) and chiral symplectic (CII) classes. Here, we consider the chiral orthogonal (BDI) case which is the…