Related papers: Mean Euler characteristic of stationary random clo…
Field electron emission from nanometer-scale objects deviates from the predictions of the classical emission theory as both the electrostatic potential curves within the tunneling region and the image potential deviates from the planar one.…
We use Stein's method to obtain bounds on the rate of convergence for a class of statistics in geometric probability obtained as a sum of contributions from Poisson points which are exponentially stabilizing, i.e. locally determined in a…
This is supplementary material for the article arxiv:0708.3250. We provide an alternative introduction of the mean Euler Characteristic, additional examples and the percolation thresholds for 2-uniform lattices.
In this article, we study several aspects of the intersections of algorithmically random closed sets. First, we answer a question of Cenzer and Weber, showing that the operation of intersecting relatively random closed sets (with respect to…
Intersection of a random fractal or self-affine set with a linear manifold or another fractal set is studied, assuming that one of the sets is in a translational motion with respect to the other. It is shown that the mass of such an…
In a closed manifold of positive dimension $n$, we estimate the expected volume and Euler characteristic for random submanifolds of codimension $r\in \{1,...,n\}$ in two different settings. On one hand, we consider a closed Riemannian…
We consider Gaussian signals, i.e. random functions $u(t)$ ($t/L \in [0,1]$) with independent Gaussian Fourier modes of variance $\sim 1/q^{\alpha}$, and compute their statistical properties in small windows $[x, x+\delta]$. We determine…
In this paper we establish a new mean field-type formulation to study the problem of prescribing Gaussian and geodesic curvatures on compact surfaces with boundary, which is equivalent to the following Liouville-type PDE with nonlinear…
A theory for the averaged optical characteristics of an ensemble of metal nanoparticles with different shapes has been developed. The theory is applicable both for the nanoparticle size at which the optical conductivity of the particle is a…
A special formula for the total mean curvature of an ovaloid is derived. This formula allows us to extend the notion of the mean curvature to the class of boundaries of strictly convex sets. Moreover, some integral formula for ovaloids is…
As generalizations of random graphs, random simplicial complexes have been receiving growing attention in the literature. In this paper, we naturally extend the Random Connection Model (RCM), a random graph that has been extensively studied…
The study of the normalized sum of random variables and its asymptotic behaviour has been and continues to be a central chapter in probability and statistical mechanics. When those variables are independent the central limit theorem ensures…
If a real value invariant of compact combinatorial manifolds (with or without boundary) depends only on the number of simplices in each dimension on the manifold, then the invariant is completely determined by Euler characteristics of the…
In this paper we study the problem of tracking the mean of a piecewise stationary sequence of independent random variables. First we consider the case where the transition times are known and show that a direct running average performs the…
In this paper we explore the algebraic structure and combinatorial properties of eulerian magnitude homology. First, we analyze the diagonality conditions of eulerian magnitude homology, providing a characterization of complete graphs.…
In this work we consider the problem of extracting a set of interaction parameters from an high-dimensional dataset describing T independent configurations of a complex system composed of N binary units. This problem is formulated in the…
Assume that the coefficients of a polynomial in a complex variable are Laurent polynomials in some complex parameters. The parameter space (a complex torus) splits into strata corresponding to different combinations of coincidence of the…
A closed form formula (generating function) for the Euler characteristic of the configuration space of $\scriptstyle n$ particles in a simplicial complex is given.
For stationary signals in time the weak law of large numbers (WLLN) states that ensemble and realization averages are within e of each other with a probability of order O(1/Ne^2) when considering N signal components. The graph WLLN…
Using Green's theorem we reduce the variation of the total mean curvature of a smooth surface in the Euclidean 3-space to a line integral of a special vector field and obtain the following well-known theorem as an immediate consequence: the…