Related papers: Stochastic bias in multi-dimensional excursion set…
The simplest stochastic halo formation models assume that the traceless part of the shear field acts to increase the initial overdensity (or decrease the underdensity) that a protohalo (or protovoid) must have if it is to form by the…
The Excursion Set approach has been used to make predictions for a number of interesting quantities in studies of nonlinear hierarchical clustering. These include the halo mass function, halo merger rates, halo formation times and masses,…
We provide a simple formula that accurately approximates the first crossing distribution of barriers having a wide variety of shapes, by random walks with a wide range of correlations between steps. Special cases of it are useful for…
Recently, we provided a simple but accurate formula which closely approximates the first crossing distribution associated with random walks having correlated steps. The approximation is accurate for the wide range of barrier shapes of…
The excursion set theory, where density perturbations evolve stochastically with the smoothing scale, provides a method for computing the dark matter halo mass function. The computation of the mass function is mapped into the so-called…
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…
In the standard excursion set model for the growth of structure, the statistical properties of halos are governed by the halo mass and are independent of the larger scale environment in which the halos reside. Numerical simulations,…
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…
We exploit the excursion set approach in integral formulation to derive novel, accurate analytic approximations of the unconditional and conditional first crossing distributions, for random walks with uncorrelated steps and general shapes…
Insight into a number of interesting questions in cosmology can be obtained from the first crossing distributions of physically motivated barriers by random walks with correlated steps. We write the first crossing distribution as a formal…
The excursion set approach provides a framework for predicting how the abundance of dark matter halos depends on the initial conditions. A key ingredient of this formalism comes from the physics of halo formation: the specification of a…
If one accounts for correlations between scales, then nonlocal, k-dependent halo bias is part and parcel of the excursion set approach, and hence of halo model predictions for galaxy bias. We present an analysis that distinguishes between a…
We present estimates of the nonlinear bias of cosmological halo formation, spanning a wide range in the halo mass from $\sim 10^{5} M_\odot$ to $\sim 10^{12} M_\odot$, based upon both a suite of high-resolution cosmological N-body…
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…
In this article, we show that a stochastic form of scale-dependent halo bias arises in multi-source inflationary models, where multiple fields determine the initial curvature perturbation. We derive this effect for general non-Gaussian…
We present a new method to compute the first crossing distribution in excursion set theory for the case of correlated random walks. We use a combination of the path integral formalism of Maggiore & Riotto, and the integral equation solution…
We describe a model of dark matter halo abundances and clustering which combines the two most widely used approaches to this problem: that based on peaks and the other based on excursion sets. Our approach can be thought of as addressing…
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…
The random walk with hyperbolic probabilities that we are introducing is an example of stochastic diffusion in a one-dimensional heterogeneous media. Although driven by site-dependent one-step transition probabilities, the process retains…
Characterizing the level of primordial non-Gaussianity (PNG) in the initial conditions for structure formation is one of the most promising ways to test inflation and differentiate among different scenarios. The scale-dependent imprint of…