An excursion set model for the distribution of dark matterand dark matter haloesRavi

A model of the gravitationally evolved dark matter distribution, in the Eulerian space, is developed. It is a simple extension of the excursion set model that is commonly used to estimate the mass function of collapsed dark matter haloes. In addition to describing the evolution of the dark matter itself, the model allows one to describe the evolution of the Eulerian space distribution of the haloes. It can also be used to describe density prooles, on scales larger than the virial radius, of these haloes, and to quantify the way in which matter ows in and out of Eulerian cells. When the initial Lagrangian space distribution is white noise Gaussian, the model suggests that the Inverse Gaussian distribution should provide a reasonably good approximation to the evolved Eulerian density eld, in agreement with numerical simulations. Application of this model to clustering from more general Gaussian initial conditions is discussed at the end.