2012/01/31 by Julien Carron, Mark C. Neyrinck · 1 citation
Mathematics · Physics and Astronomy · #Connection (principal bundle) #Correlation function (quantum field theory) #Cosmology and Gravitation Theories #Field (mathematics) #Galaxies: Formation, Evolution, Phenomena #Hierarchy #Log-normal distribution #Mathematics #Nonlinear system #Observable #Perturbation theory (quantum mechanics) #Physics #Pure mathematics #Quantum mechanics #Scientific Research and Discoveries #Statistical physics #Statistics #Theoretical physics #astro-ph.CO #physics.data-an
paper · pdf · doi:10.1088/0004-637x/750/1/28
published as ApJ, 750, 28 (2012) · 10 pages, 3 figures, matches version accepted for publication by ApJ. Some editing in the conclusion and minor changes w.r.t. v1
arxiv created 2012/02/24 · openalex publication_date 2012/04/12 · arxiv updated 2012/04/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Motivated by recent results on lognormal statistics showing that the moment hierarchy of a lognormal variable completely fails at capturing its information content in the large variance regime, in this work we discuss the inadequacy of the hierarchy of correlation functions to describe a correlated lognormal field, which provides a roughly accurate description of the nonlinear cosmological matter density field. We present families of fields having the same hierarchy of correlation functions than the lognormal field at all orders. This explicitly demonstrates the little studied though known fact that the correlation function hierarchy never provides a complete description of a lognormal field, and that it fails to capture information in the nonlinear regime, where other simple observables are left totally unconstrained. We discuss why perturbative, Edgeworth-like approaches to statistics in the nonlinear regime, common in cosmology, can never reproduce or predict that effect, and why it is, however, generic for tailed fields, hinting at a breakdown of the perturbation theory based on the field fluctuations. We make a rough but successful quantitative connection to N -body simulations results that showed that the spectrum of the log-density field carries more information than the spectrum of the field entering the nonlinear regime.