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We introduce grlic, a publicly available Python tool for generatingglass-like point distributions with a radial density profile $n(r)$ as it isobserved in large-scale surveys of galaxy distributions on the past light cone.Utilising these glass-like catalogues, we assess the bias and variance of theLandy-Szalay (LS) estimator of the first three two-point correlation function(2PCF) multipoles in halo and particle catalogues created with the cosmologicalN-body code gevolution. Our results demonstrate that the LS estimatorcalculated with the glass catalogues is biased by less than $10^{-4}$ withrespect to the estimate derived from Poisson-sampled random catalogues, for allmultipoles considered and on all but the smallest scales. Additionally, theestimates derived from glass-like catalogues exhibit significantly smallerstandard deviation $\sigma$ than estimates based on commonly usedPoisson-sampled random catalogues of comparable size. The standard deviation ofthe estimate depends on a power of the number of objects $N_R$ in the randomcatalogue; we find a power law $\sigma \propto N_R^{-0.9}$ for glass-likerandom catalogues as opposed to $\sigma \propto N_R^{-0.48}$ usingPoisson-sampled random catalogues. Given a required precision, this allows fora much reduced number of objects in the glass-like random catalogues used forthe LS estimate of the 2PCF multipoles, significantly reducing thecomputational costs of each estimate.

Glass-Like Random Catalogues for Two-Point Estimates on the Light Cone