TY - JOUR A1 - Schmiedt, Anja Bettina A1 - Weiß, Christian T1 - The pair correlation function of multi-dimensional low-discrepancy sequences with small stochastic error terms JF - Journal of Number Theory N2 - In any dimension d≥2, there is no known example of a low-discrepancy sequence which possesses Poisssonian pair correlations. This is in some sense rather surprising, because low-discrepancy sequences always have β-Poissonian pair correlations for all 0<β<1/d and are therefore arbitrarily close to having Poissonian pair correlations (which corresponds to the case β=1/d). In this paper, we further elaborate on the closeness of the two notions. We show that d-dimensional Kronecker sequences for badly approximable vectors α→ with an arbitrary small uniformly distributed stochastic error term generically have β=1/d-Poissonian pair correlations. KW - Kronecker sequences KW - Poissonian pair correlations KW - Uniform distribution Y1 - 2024 U6 - https://doi.org/10.1016/j.jnt.2023.12.011 VL - 259 SP - 422 EP - 437 ER -