AAS 201st Meeting, January, 2003
Session 59. Structure in and at Clusters of Galaxies
Oral, Tuesday, January 7, 2003, 10:00-11:30am, 606-607

## [59.02] One-point Statistics of the Cosmic Density Field in Real and Redshift Spaces with A Multiresolutional Decomposition

H. Zhan, L.Z. Fang (Dept of Physics, Univ of Arizona)

A method of performing the one-point statistics of the cosmic density field is developed with a multiresolutional decomposition based on the discrete wavelet transform (DWT). The algorithm for recovering the DWT one-point statistics from redshift distortion is also derived. Tests on N-body simulations show that this algorithm works well on scales from a few hundred to a few h-1 Mpc for popular cold dark matter models. The same recovery can be applied to the rms density fluctuation within a given radius.

One can design model independent estimators of the redshift distortion parameter (\beta) from combinations of DWT modes in redshift space. When the non-linear redshift distortion is not negligible, the traditional estimator from quadrupole-to-monopole ratio needs additional information about the scale-dependence, such as the power-spectrum index or the real-space correlation function of the random field. The DWT \beta estimators, however, do not need such extra information. Numerical tests show that the proposed DWT estimators are able to determine \beta with less than 15% uncertainty in the redshift range 0 \leq z \leq 3.