Related papers: One step beyond: The excursion set approach with c…
We study the effects of primordial non-Gaussianity on the large scale structure in the excursion set approach, accounting for correlations between steps of the random walks in the smoothed initial density field. These correlations are…
Recent analytical work on the modelling of dark halo abundances and clustering has demonstrated the advantages of combining the excursion set approach with peaks theory. We extend these ideas and introduce a model of excursion set peaks…
A classic method for computing the mass function of dark matter halos is provided by excursion set theory, where density perturbations evolve stochastically with the smoothing scale, and the problem of computing the probability of halo…
Excursion set theory, where density perturbations evolve stochastically with the smoothing scale, provides a method for computing the mass function of cosmological structures like dark matter halos, sheets and filaments. The computation of…
We discuss in the framework of the excursion set formalism a recent discovery from N-body simulations that the clustering of haloes of given mass depends on their formation history. We review why the standard implementation of this…
We show how correlated steps introduces significant contributions to the modification of the halo mass function in modified gravity models, taking the chameleon models as an example, in the framework of the excursion set approach. This…
I review the excursion set theory (EST) of dark matter halo formation and clustering. I recount the Press-Schechter argument for the mass function of bound objects and review the derivation of the Press-Schechter mass function in EST. The…
In excursion set theory the computation of the halo mass function is mapped into a first-passage time process in the presence of a barrier, which in the spherical collapse model is a constant and in the ellipsoidal collapse model is a fixed…
Excursion set theory is a powerful and widely used tool for describing the distribution of dark matter haloes, but it is normally applied with simplifying approximations. We use numerical sampling methods to study the mass functions…
In this paper, we study the scaling limit of a class of random walks which behave like simple random walks outside of a bounded region around the origin and which are subject to a partial reflection near the origin. If the probability of…
Relying on the excursion set theory, we compute the number density of local extrema and crossing statistics versus the threshold for the stock market indices. Comparing the number density of excursion sets calculated numerically with the…
We derive approximated, yet very accurate analytical expressions for the abundance and clustering properties of dark matter halos in the excursion set peak framework; the latter relies on the standard excursion set approach, but also…
The excursion set theory based on spherical or ellipsoidal gravitational collapse provides an elegant analytic framework for calculating the mass function and the large-scale bias of dark matter haloes. This theory assumes that the…
Our heuristic understanding of the abundance of dark matter halos centers around the concept of a density threshold, or "barrier", for gravitational collapse. If one adopts the ansatz that regions of the linearly evolved density field…
Analytical approaches to galaxy formation and reionization are based on the mathematical problem of random walks with barriers. The statistics of a single random walk can be used to calculate one-point distributions ranging from the mass…
We present a new algorithm to sample the constrained eigenvalues of the initial shear field associated with Gaussian statistics, called the `peak/dip excursion-set-based' algorithm, at positions which correspond to peaks or dips of the…
Virtually all the emergent properties of a complex system are rooted in the non-homogeneous nature of the behaviours of its elements and of the interactions among them. However, the fact that heterogeneity and correlations can appear…
In this paper, we study the overlap distribution and Gibbs measure of the Branching Random Walk with Gaussian increments on a binary tree. We first prove that the Branching Random Walk is 1 step Replica Symmetry Breaking and give a precise…
Aims. We aim to study the stochastic evolution of the smoothed overdensity $\delta$ at scale $S$ of the form $\delta(S) = \int_{0}^S K(S,u)\mathrm{d}W(u)$, where $K$ is a kernel and $\mathrm{d}W$ is the usual Wiener process. Methods. For a…
A random walk generated by a sum of independent identity distributed random variables with positive expectation is considered. The limiting distributions for the first- passage -time of a step-function boundary are derived.