A U-statistic of a Poisson point process is defined as the sum ∑ f (x₁, · · ·, xk) over all (possibly infinitely many) k-tuples of distinct points of the point process. Using the Malliavin calculus, ...

An understanding of a material's microscopic architecture is important to improve its mechanical properties. Poisson's ratio, which celebrates its bicentenary this year, continues to provide a good ...

This paper establishes expectation and variance asymptotics for statistics of the Poisson-Voronoi approximation of general sets, as the underlying intensity of the Poisson point process tends to ...