Large deviation principle at work: Computation of the statistical properties of the exact one-point aperture mass
Large deviation principle at work: Computation of the statistical properties of the exact one-point aperture mass
复制标题
工作中的大偏差原理：计算精确单点孔径质量的统计特性
DOI：
--
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
F. Bernardeau
中科院分区：
文献类型：
--
作者：
P. Reimberg;F. Bernardeau
本文提出了一个通用的形式主义，允许的累积量生成函数和一点概率分布函数（PDF）的孔质量（$hat M$$_{ap}$），一个共同的观测宇宙剪切观测的推导。我们的形式主义是基于大偏差原理（LDP）适用于，在这样的宇宙学背景下，任意一组同心细胞的密度。我们在这里表明，LDP确实可以用于一个更大的家庭比以前设想的可观测量，如那些建立从连续和非线性泛函的密度分布。可观测孔径质量的一般表达式取决于约化的剪切剖面，使其成为投影密度场的一个相当复杂的函数。由于这个困难，通常采用的近似包括在忽略非线性效应的情况下，用这种结构中的剪力代替减小的剪力。我们能够精确地量化这种近似如何影响$hat M$$_{ap}$统计特性。特别是，我们推导出$hat M$$_{ap}$偏斜度的校正项并重建其单点PDF。
This paper presents a general formalism that allows the derivation of the cumulant generating function and one-point Probability Distribution Function (PDF) of the aperture mass ($hat M$$_{ap}$), a common observable for cosmic shear observations. Our formalism is based on the Large Deviation Principle (LDP) applied, in such cosmological context, to an arbitrary set of densities in concentric cells. We show here that the LDP can indeed be used for a much larger family of observables than previously envisioned, such as those built from continuous and nonlinear functionals of the density profiles. The general expression of the observable aperture mass depends on reduced shear profile making it a rather involved function of the projected density field. Because of this difficulty, an approximation that is commonly employed consists in replacing the reduced shear by the shear in such a construction neglecting therefore non-linear effects. We were precisely able to quantify how this approximation affects the $hat M$$_{ap}$ statistical properties. In particular we derive the corrective term for the skewness of the $hat M$$_{ap}$ and reconstruct its one-point PDF.