4 papers
Minimax estimation of the structure factor of spatial point processes
Gabriel Mastrilli
We investigate the problem of estimating the structure factor, or spectra, of stationary spatial point processes. In the first part, we establish a minimax lower bound for this est…
Asymptotic fluctuations of smooth linear statistics of independently perturbed lattices
Gabriel Mastrilli
We consider the hyperuniform model of d-dimensional integer lattice perturbed by independent random variables and we investigate the large scale asymptotic fluctuations of smoothed…
Estimating the hyperuniformity exponent of point processes
Gabriel Mastrilli, Bartłomiej Błaszczyszyn, Frédéric Lavancier
We address the challenge of estimating the hyperuniformity exponent of a spatial point process, given only one realization of it. Assuming that the structure factor of the…
Repelled point processes with application to numerical integration
Diala Hawat, Gabriel Mastrilli, Rémi Bardenet +1
We look at Monte Carlo numerical integration from a stochastic geometry point of view. While crude Monte Carlo estimators relate to linear statistics of a homogeneous Poisson point…