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**Session 94 - Large-Scale Structure: Observations and Theory.**

*Oral session, Wednesday, January 17*

*Corte Real, Hilton*

## [94.06] Hierarchical clustering and a detailed description of the merger history tree

*R. K. Sheth (U.C. Berkeley)*
The Press--Schechter description of gravitational clustering from an initially
Poisson distribution is equivalent to the well studied Galton--Watson branching
process. This correspondence is used to provide a detailed description of the
evolution of hierarchical clustering, including a complete description of the
merger history tree. An analytic expression for the merger history of any
given Poisson Press--Schechter clump is obtained. This expression allows one
to calculate the partition function of merger history trees. The distribution
function of counts in randomly placed cells, as a function of time, is also
obtained. Thus, the Press--Schechter description of the gravitational
evolution of clustering from an initially Poisson distribution is now complete.
The detailed predictions of the model are in good agreement with N-body
simulations. One way to extend these results to more general Gaussian initial
conditions is discussed. The counts in cells distribution derived here is in
good agreement with the observed distribution of galaxies. One example of the
usefulness of knowing the merger history tree is that it allows one to explain
and quantify observations at relatively high redshift such as the
Butcher--Oemler effect.

**Program
listing for Wednesday**