Related papers: Fractal random series generated by Poisson-Voronoi…
In this paper, we consider a Riemannian manifold $M$ and the Poisson-Voronoi tessellation generated by the union of a fixed point $x_0$ and a Poisson point process of intensity $\lambda$ on $M$. We obtain asymptotic expansions up to the…
We establish several new fractal and number theoretical phenomena connected with expansions which are generated by infinite linear iterated function systems. First of all we show that the systems $\Phi$ of cylinders of generalized L\"uroth…
In this article, we introduce fractional Poisson felds of order k in n-dimensional Euclidean space $R_n^+$. We also work on time-fractional Poisson process of order k, space-fractional Poisson process of order k and tempered version of…
The Voronoi tessellation of a homogeneous Poisson point process in the lower half-plane gives rise to a family of vertical elongated cells in the upper half-plane. The set of edges of these cells is ruled by a Markovian branching mechanism…
We consider several different models for generating random fractals including random self-similar sets, random self-affine carpets, and fractal percolation. In each setting we compute either the \emph{almost sure} or the \emph{Baire…
We bridge the properties of the regular square and honeycomb Voronoi tessellations of the plane to those of the Poisson-Voronoi case, thus analyzing in a common framework symmetry-break processes and the approach to uniformly random…
In this article a collection of random self-similar fractal dendrites is constructed, and their Hausdorff dimension is calculated. Previous results determining this quantity for random self-similar structures have relied on geometrical…
In this paper, we introduce a family of discrete rectangular uniform distributions on the natural numbers-referred to as orthogonal dice-characterized by the property that their means equal their variances. These distributions arise…
We define a general class of random systems of horizontal and vertical weighted broken lines on the quarter plane whose distribution are proved to be translation invariant. This invariance stems from a reversibility property of the model.…
We consider the Voronoi diagram generated by $n$ i.i.d. $\mathbb{R}^{d}$-valued random variables with an arbitrary underlying probability density function $f$ on $\mathbb{R}^{d}$, and analyse the asymptotic behaviours of certain geometric…
We propose a distribution-free approach to the study of random geometric graphs. The distribution of vertices follows a Poisson point process with intensity function $nf(\cdot)$, where $n\in \mathbb{N}$, and $f$ is a probability density…
We study Poisson--Voronoi percolation and its discrete analogue Bernoulli--Voronoi percolation in spaces with a non-amenable product structure. We develop a new method of proving smallness of the uniqueness threshold $p_u(\lambda)$ at small…
This paper is concerned mainly with the macroscopic fractal behavior of various random sets that arise in modern and classical probability theory. Among other things, it is shown here that the macroscopic behavior of Boolean coverage…
The interest in orthogonal polynomials and random Fourier series in numerous branches of science and a few studies on random Fourier series in orthogonal polynomials inspired us to focus on random Fourier series in Jacobi polynomials. In…
In their 1993 paper, Arak, Clifford and Surgailis discussed a new model of random planar graph. As a particular case, that model yields tessellations with only T-vertices (T-tessellations). Using a similar approach involving Poisson lines,…
We define a class of random measures, spatially independent martingales, which we view as a natural generalisation of the canonical random discrete set, and which includes as special cases many variants of fractal percolation and Poissonian…
We investigate the high-dimensional asymptotic distributional behavior of the $\mathbf{f}$-vector of a random Vietoris-Rips complex, that is generated over a stationary Poisson point process in $[-\frac{1}{2}, \frac{1}{2}]^d$ as the space…
Given a Poisson process on a bounded interval, its random geometric graph is the graph whose vertices are the points of the Poisson process and edges exist between two points if and only if their distance is less than a fixed given…
We analyze a class of spatial random spanning trees built on a realization of a homogeneous Poisson point process of the plane. This tree has a simple radial structure with the origin as its root. We first use stochastic geometry arguments…
We construct first a class of Moran fractals in R^d with countably many generators and non-stationary contraction rates; at each step n, the contractions depend on n-truncated sequences, and are related to asymptotic letter frequencies. In…