**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
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## [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.

The author(s) of this abstract have provided an email address
for comments about the abstract:
zhanhu@physics.arizona.edu

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Bulletin of the American Astronomical Society, **34**, #4

© 2002. The American Astronomical Soceity.