ﻻ يوجد ملخص باللغة العربية
Let ${B(xi_n,r_n)}_{nge1}$ be a sequence of random balls whose centers ${xi_n}_{nge1}$ is a stationary process, and ${r_n}_{nge1}$ is a sequence of positive numbers decreasing to 0. Our object is the random covering set $E=limsuplimits_{ntoinfty}B(xi_n,r_n)$, that is, the points covered by $B(xi_n,r_n)$ infinitely often. The sizes of $E$ are investigated from the viewpoint of measure, dimension and topology.
Geometric properties of $N$ random points distributed independently and uniformly on the unit sphere $mathbb{S}^{d}subsetmathbb{R}^{d+1}$ with respect to surface area measure are obtained and several related conjectures are posed. In particular, we d
We consider a variant of a classical coverage process, the boolean model in $mathbb{R}^d$. Previous efforts have focused on convergence of the unoccupied region containing the origin to a well studied limit $C$. We study the intersection of sets cent
The results of this paper are 3-folded. Firstly, for any stationary determinantal process on the integer lattice, induced by strictly positive and strictly contractive involution kernel, we obtain the necessary and sufficient condition for the $psi$-
We prove that random walks in random environments, that are exponentially mixing in space and time, are almost surely diffusive, in the sense that their scaling limit is given by the Wiener measure.
We consider the convex hull of the perturbed point process comprised of $n$ i.i.d. points, each distributed as the sum of a uniform point on the unit sphere $S^{d-1}$ and a uniform point in the $d$-dimensional ball centered at the origin and of radiu