4 papers
Jittered sampling and probability measures
Roberto Bramati, Luca Brandolini, Giancarlo Travaglini
This paper investigates the discrepancy of a family of random sampling methods obtained by perturbing the grid , where …
Discrepancy estimates for multi-dimensional non-smooth convex bodies: a case study
Roberto Bramati, Luca Brandolini, Alessandro Monguzzi
We study -averaged discrepancies of finite sequences of points in the torus with respect to translated and dilated copies of convex bodies with non-smooth bound…
On a discrete approach to lower bounds in discrepancy theory
Luca Brandolini, Bianca Gariboldi, Giacomo Gigante +1
In this paper, we prove that some renowned lower bounds in discrepancy theory admit a discrete analogue. Namely, we prove that the lower bound of the discrepancy for corners in the…
Irregularities of distribution and Fourier transforms of multi-dimensional convex bodies
Luca Brandolini, Leonardo Colzani, Giancarlo Travaglini
W. Schmidt, H. Montgomery, and J. Beck proved a result on irregularities of distribution with respect to -dimensional balls. In this paper, we extend their result to any -dim…