Городской семинар по теории вероятностей и математической статистике

«Asymptotic Variance of Higher order Statistics of Point processes»
F. Frommer

18 сентября в 18:00
Наб. р. Фонтанки, 27, ауд. 311

We investigate statistical properties of certain stationary point processes, including determinantal processes with projection kernels, Gibbs point processes with superstable pair interactions and the perturbed lattice. These are examples of hyperuniform and non-hyperuniform stationary point processes, respectively. We are interested in the variances of their second and (higher order) statistics within a ball around the origin, and we study the asymptotic growth of this variance as the radius of the ball goes to infinity. For Gibbs processes with superstable interactions these results have an interesting application to the so-called inverse Henderson problem of statistical mechanics.