The excursion set model a step beyond: Environmental dependence

Abstract: In terms of the excursion set model, we used Monte Carlo methods in order to study the non-Markovian stochastic evolution of the smoothed overdensity $\delta$ at scale $S$. For a Gaussian density field, smoothed by the top-hat filter, in real space, we used random walks, with the correct correlation between scales, in order to calculate constrained probabilities and to connect the number of structures with the overdensity of their environment. A constant barrier is used, lower than the usual one but which improves the consistency of our results with those of N-body simulations.We present comparisons of multiplicity functions with those resulting from N-body simulations as well as number densities of descendant haloes and of their progenitors and we connect them to the density of their large environment.There exists a dependence of the number of haloes on their environment which is different for different masses of these haloes.This number increases for larger overdensity of the environment for large haloes and decreases for small ones. The number of progenitors of these haloes is insensitive to the overdensity of their large environment.