2003/08/31 by Hiroko Koyama, Taihei Yano
Economics, Econometrics and Finance · Environmental Science · Physics and Astronomy · #Climate variability and models #Complex Systems and Time Series Analysis #Cosmology and Gravitation Theories #astro-ph #gr-qc #nlin.CD #nlin.PS
paper · pdf · doi:10.1086/423262
published as Astrophys.J. 624 (2005) 1-6 · 16 pages, 4 figures. Accepted for publication in APJ. Some sentences and figures are revised
openalex publication_date 2005/04/20 · arxiv created 2005/06/15 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31
The connection between the two-point and the three-point correlation functions in the nonlinear gravitational clustering regime is studied. Under a scaling hypothesis, we find that the three-point correlation function, ζ, obeys the scaling law ζ ∝ ξ (3 m +4 w -2 )/(2 m +2 w ) in the nonlinear regime, where ξ, m , w , and are the two-point correlation function, the power index of the power spectrum in the nonlinear regime, the number of spatial dimensions, and the power index of the phase correlations, respectively. The new formula reveals the origin of the power index of the three-point correlation function. We also obtain the theoretical condition for which the "hierarchical form" ζ ∝ ξ 2 is reproduced.