The forest of merger history trees associated with the formation of dark   matter halos
  We describe a simple efficient algorithm that allows one to construct Monte-Carlo realizations of merger histories of dark matter halos. The algorithm is motivated by the excursion set model (Bond et al. 1991) for the conditional and unconditional halo mass functions. The forest of trees constructed using this algorithm depends on the underlying power spectrum. For Poisson or white-noise initial power-spectra, the forest has exactly the same properties as the ensemble of trees described by Sheth (1996) and Sheth & Pitman (1997). In this case, many ensemble averaged higher order statistics of the tree distribution can be computed analytically. For Gaussian initial conditions with more general power-spectra, mean properties of the ensemble closely resemble the mean properties expected from the excursion set approach. Various statistical quantities associated with the trees constructed using our algorithm are in good agreement with what is measured in numerical simulations of hierarchical gravitational clustering. 
Ravi K. Sheth & Gerard Lemson