e-Nets and Simplex Range Queries.
Estimating an even spherical measure from its sine transform
To reconstruct an even Borel measure on the unit sphere from finitely many values of its sine transform a least square estimator is proposed. Applying results by Gardner, Kiderlen and Milanfar we estimate its rate of convergence and prove strong consistency. We close this paper by giving an estimator for the directional distribution of certain three-dimensional stationary Poisson processes of convex cylinders which have applications in material science.
Eulersche Charakteristik, Projektionen und Quermaßintegrale.
Expectation of Random Polytopes.
Extremal 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 . We show that in order for the probability to be roughly , the number of steps of the random walk should be between and for some constant . As a result, we attain a bound for the -covering time of a spherical Brownian motion.