no code implementations • 19 Feb 2021 • Alexander Marynych, Ilya Molchanov
We show that in this case the set of $x\in\mathbb{R}^d$ such that $x+K$ contains the sample $\Xi_n$, upon multiplying by $n$, converges in distribution to the zero cell of a certain Poisson hyperplane tessellation.
Metric Geometry Probability Primary: 60D05, secondary: 52A22, 52B05
no code implementations • 13 Jan 2021 • Chinmoy Bhattacharjee, Ilya Molchanov
We consider the Gaussian approximation for functionals of a Poisson process that are expressible as sums of region-stabilizing (determined by the points of the process within some specified regions) score functions and provide a bound on the rate of convergence in the Wasserstein and the Kolmogorov distances.
Probability 60F05
