http://arxiv.org/abs/2203.13288
We show how to increase the accuracy of estimates of the two-point correlation function without sacrificing efficiency. We quantify the error of the pair-counts and of the Landy-Szalay estimator by comparing with exact reference values. The standard method, using random point sets, is compared to geometrically motivated estimators and estimators using quasi Monte-Carlo integration. In the standard method the error scales proportional to $1/\sqrt{N_r}$, with $N_r$ the number of random points. In our improved methods the error is scaling almost proportional to $1/N_q$, where $N_q$ is the number of points from a low discrepancy sequence. In an example we achieve a speedup by a factor of $10^4$ over the standard method, still keeping the same level of accuracy. We also discuss how to apply these improved estimators to incompletely sampled galaxy catalogues.
M. Kerscher
Mon, 28 Mar 22
45/50
Comments: 11 pages, 6 figures, submitted to A&A
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