24 citations · 60 across the 18 of their papers we have counts for
25 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…
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…
Single radius spherical cap discrepancy on compact two-point homogeneous spaces
Luca Brandolini, Bianca Gariboldi, Giacomo Gigante +1
In this note we study estimates from below of the single radius spherical discrepancy in the setting of compact two-point homogeneous spaces. Namely, given a -dimensional manifo…
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…
Discrepancy and approximation of absolutely continuous measures with atomic measures
Luca Brandolini, Leonardo Colzani, Giancarlo Travaglini
We prove several results concerning the discrepancy, tested on balls in the -dimensional torus , between absolutely continuous measures and finite atomic measure…