Abstract

The abundance of halos of a given mass and their statistical correlations are important tools to probe the initial conditions of the process of structure formation, and thus to investigate the properties (like the amount of non-Gaussianity) of the primordial cosmological perturbation that seeds it. In the excursion set framework, the average of the matter density field over the volume corresponding to a mass scale fluctuates randomly as the smoothing scale changes. The abundance of halos is mapped into the rate at which these random trajectories first cross a suitable threshold. For physically motivated choices of the filter function to be used for the averaging, the steps of the walks are correlated and the first crossing problem becomes of difficult solution. I will discuss how to set up an expansion scheme to deal with these correlations for a Gaussian process, and how non-Gaussianity can easily be included. Some extensions of this approach to describe other fundamental probes of the initial seeds of the Large Scale Structures (like the halo bias) will also be presented.