Optimization of Tessellation-based Statistics: Void Statistics

Tessellation methods are extensively employed in the analyses of cosmic large-scale structure. However, these techniques are highly sensitive to perturbations in both densities and positions of points, often leading to substantial rearrangements of tessellation configurations. As a result, considerable additional statistical errors are introduced in various tessellation-based statistics, thereby weakening their cosmological constraints. In this work, we identify this issue and propose an efficacious measurement scheme through subsampling and averaging to enhance the stabilities of tessellation-based statistics. As a case study, we apply the new scheme to measure multiple primary void statistics (i.e., void size function, void two-point correlation function, and void power spectrum) in two distinct classes of voids, based on Delaunay and Voronoi tessellations, respectively. We notice that the statistical uncertainties in void statistics can be predominantly attributed to tessellation instabilities. Through rigorous testing, we demonstrate that the proposed method can substantially eliminate these scatters to deeply mine the statistical power of void statistics. Specifically, we find that our method can dramatically boost the signal-to-noise ratios of void baryon acoustic oscillations and significantly improve the constraining power of void statistics on cosmological parameters. These findings showcase the enormous application potential of our new method in maximizing extraction of cosmological information from galaxy surveys. Importantly, our method is simple yet highly potent with broad applicability, hopefully evolving into a standard framework for measuring tessellation-based statistics in the future.