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arXiv · 2108.01673

Indicator Power Spectra: Surgical Excision of Non-linearities and Covariance Matrices for Counts in Cells

Andrew Repp·István Szapudi
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Abstract

We here introduce indicator functions, which identify regions of a given density in order to characterize the density dependence of clustering. After a general introduction to this tool, we show that indicator-function power spectra are biased versions of the linear spectrum on large scales. We provide a calculation from first principles for this bias, we show that it reproduces simulation results, and we provide a simple functional form for the translinear portion of the indicator-function spectra. We also outline two applications: first, these spectra facilitate surgical excision of non-linearity and thus significantly increase the reach of linear theory. Second, indicator-function spectra permit calculation of theoretical covariance matrices for counts-in-cells (CIC), facilitating parameter estimation with complementary CIC methods.

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Andrew Repp, István Szapudi. 2021-08-03. Indicator Power Spectra: Surgical Excision of Non-linearities and Covariance Matrices for Counts in Cells. https://doi.org/10.1093/mnras/stab3031

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