{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/computing-the-small-scale-galaxy-power","title":"Computing the Small-Scale Galaxy Power Spectrum and Bispectrum in Configuration-Space","arxiv_id":"1912.01010","date":"2019-12-02","proceeding":null,"authors":["Oliver H. E. Philcox","Daniel J. Eisenstein"],"abstract":"We present a new class of estimators for computing small-scale power spectra and bispectra in configuration-space via weighted pair- and triple-counts, with no explicit use of Fourier transforms. Particle counts are truncated at $R_0\\sim 100h^{-1}\\,\\mathrm{Mpc}$ via a continuous window function, which has negligible effect on the measured power spectrum multipoles at small scales. This gives a power spectrum algorithm with complexity $\\mathcal{O}(NnR_0^3)$ (or $\\mathcal{O}(Nn^2R_0^6)$ for the bispectrum), measuring $N$ galaxies with number density $n$. Our estimators are corrected for the survey geometry and have neither self-count contributions nor discretization artifacts, making them ideal for high-$k$ analysis. Unlike conventional Fourier transform based approaches, our algorithm becomes more efficient on small scales (since a smaller $R_0$ may be used), thus we may efficiently estimate spectra across $k$-space by coupling this method with standard techniques. We demonstrate the utility of the publicly available power spectrum algorithm by applying it to BOSS DR12 simulations to compute the high-$k$ power spectrum and its covariance. In addition, we derive a theoretical rescaled-Gaussian covariance matrix, which incorporates the survey geometry and is found to be in good agreement with that from mocks. Computing configuration- and Fourier-space statistics in the same manner allows us to consider joint analyses, which can place stronger bounds on cosmological parameters; to this end we also discuss the cross-covariance between the two-point correlation function and the small-scale power spectrum.","url_abs":"https://arxiv.org/abs/1912.01010v1","url_pdf":"https://arxiv.org/pdf/1912.01010v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"computing-the-small-scale-galaxy-power","repo_url":"https://github.com/oliverphilcox/RascalC","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"computing-the-small-scale-galaxy-power","repo_url":"https://github.com/oliverphilcox/HIPSTER","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}