Poisson asymptotics for random projections of points on a high-dimensional sphere
نویسندگان
چکیده
Project a collection of points on the high-dimensional sphere onto a random direction. If most of the points are sufficiently far from one another in an appropriate sense, the projection is locally close in distribution to the Poisson point process.
منابع مشابه
Investigation of pore-scale random porous media using lattice boltzmann method
The permeability and tortuosity of pore-scale two and three-dimensional random porous media were calculated using the Lattice Boltzmann method (LBM). Effects of geometrical parameters of medium on permeability and tortuosity were investigated as well. Two major models of random porous media were reconstructed by computerized tomography method: Randomly distributed rectangular obstacles in a uni...
متن کاملSpatial statistics for lattice points on the sphere I: Individual results
We study the spatial distribution of point sets on the sphere obtained from the representation of a large integer as a sum of three integer squares. We examine several statistics of these point sets, such as the electrostatic potential, Ripley's function, the variance of the number of points in random spherical caps, and the covering radius. Some of the results are conditional on t...
متن کاملExtremal points of high dimensional random walks and mixing times of a brownian motion on the sphere
We derive asymptotics for the probability that the origin is an extremal point of a random walk in R. We show that in order for the probability to be roughly 1/2, the number of steps of the random walk should be between e logn) and e logn for some constant C > 0. As a result, we attain a bound for the π 2 -covering time of a spherical brownian motion.
متن کاملTwo-node fluid network with a heavy-tailed random input: the strong stability case
We consider a two-node fluid network with batch arrivals of random size having a heavy-tailed distribution. We are interested in the tail asymptotics for the stationary distribution of a two-dimensional queue-length process. The tail asymptotics have been well studied for two-dimensional reflecting processes where jumps have either a bounded or an unbounded light-tailed distribution. However, p...
متن کامل1 9 Fe b 20 07 Variance asymptotics and central limit theorems for generalized growth processes with applications to convex hulls and maximal points
We show that the random point measures induced by vertices in the convex hull of a Poisson sample on the unit ball, when properly scaled and centered, converge to those of a mean zero Gaussian field. We establish limiting variance and covariance asymptotics in terms of the density of the Poisson sample. Similar results hold for the point measures induced by the maximal points in a Poisson sampl...
متن کامل