Covariances of density probability distribution functions. Lessons from hierarchical models
نویسندگان
چکیده
Context . Statistical properties of the cosmic density fields are to a large extent encoded in shape one-point probability distribution functions (PDF) as measured surveys. In order successfully exploit such observables, detailed functional form covariance matrix PDF is needed. Aims The objectives model this for general stochastic and that reproduce expected cosmology. accuracy proposed forms evaluated specific cases. Methods study was conducted cosmological context determined whether defined absolutely or relatively sample mean density. Leading subleading contributions were identified within class models, so-called hierarchical models. They come from either short separation contributions. validity assessed with help toy model, minimum tree which corpus exact results could be obtained (forms one- two-point PDF, large-scale density-bias functions, full PDF). Results It first shown elements directly related spatial average sample. dominant contribution explicitly given models (coming scale contribution), leads construction functions. However, alone cannot used construct an operational likelihood function. Subdominant effects found provide corrective terms, but also priori lead limited information on matrix. Short distance more important difficult derive they depend details model. simple generic these proposed. Detailed comparisons Rayleigh-Levy flight show capture bulk supersample that, by adding short-distance contributions, qualitatively correct function can obtained.
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ژورنال
عنوان ژورنال: Astronomy and Astrophysics
سال: 2022
ISSN: ['0004-6361', '1432-0746']
DOI: https://doi.org/10.1051/0004-6361/202142526