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Convergence of randomly oscillating point patterns to the Poisson point process

Jan Rataj, Ivan Saxl, Karol Pelikán (1993)

Applications of Mathematics

Oscillating point patterns are point processes derived from a locally finite set in a finite dimensional space by i.i.d. random oscillation of individual points. An upper and lower bound for the variation distance of the oscillating point pattern from the limit stationary Poisson process is established. As a consequence, the true order of the convergence rate in variation norm for the special case of isotropic Gaussian oscillations applied to the regular cubic net is found. To illustrate these theoretical...

Convergence theorems for set-valued conditional expectations

Nikolaos S. Papageorgiou (1993)

Commentationes Mathematicae Universitatis Carolinae

In this paper we prove two convergence theorems for set-valued conditional expectations. The first is a set-valued generalization of Levy’s martingale convergence theorem, while the second involves a nonmonotone sequence of sub σ -fields.

Cyclic random motions in ℝ d -space with n directions

Aimé Lachal (2006)

ESAIM: Probability and Statistics

We study the probability distribution of the location of a particle performing a cyclic random motion in ℝ d . The particle can take n possible directions with different velocities and the changes of direction occur at random times. The speed-vectors as well as the support of the distribution form a polyhedron (the first one having constant sides and the other expanding with time t). The distribution of the location of the particle is made up of two components: a singular component (corresponding...

Determinantal probability measures

Russell Lyons (2003)

Publications Mathématiques de l'IHÉS

Determinantal point processes have arisen in diverse settings in recent years and have been investigated intensively. We study basic combinatorial and probabilistic aspects in the discrete case. Our main results concern relationships with matroids, stochastic domination, negative association, completeness for infinite matroids, tail triviality, and a method for extension of results from orthogonal projections to positive contractions. We also present several new avenues for further investigation,...

Dimension de Hausdorff de certains fractals aléatoires

Fathi Ben Nasr (1992)

Journal de théorie des nombres de Bordeaux

On construit des ensembles de Cantor aléatoires par partages successifs de rectangles, en partant d’un carré, (le nombre de divisions de la longueur peut être différent de celui de la largeur). La construction est stationnaire : elle fait intervenir des variables aléatoires indépendantes et équidistribuées. Sur ces ensembles il existe une mesure naturelle, μ , aléatoire elle aussi. Des résultats concernant les boréliens portant μ et leur dimension de Hausdorff ont déjà été obtenus par J. Peyrière...

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