@article{SchmiedtWeiss2024, author = {Schmiedt, Anja Bettina and Weiß, Christian}, title = {The pair correlation function of multi-dimensional low-discrepancy sequences with small stochastic error terms}, series = {Journal of Number Theory}, volume = {259}, journal = {Journal of Number Theory}, doi = {10.1016/j.jnt.2023.12.011}, pages = {422 -- 437}, year = {2024}, abstract = {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.}, language = {en} }