Related papers: Excursion Set Theory for generic moving barriers a…
Analytic models based on spherical and ellipsoidal gravitational collapse have been used to derive the mass functions of dark matter halos and their progenitors (the conditional mass function). The ellipsoidal model generally provides a…
The statistical tools needed to obtain a mass function from realistic collapse time estimates are presented. Collapse dynamics has been dealt with in paper I of this series by means of the powerful Lagrangian perturbation theory and the…
We use the concept of excursions for the prediction of random variables without any moment existence assumptions. To do so, an excursion metric on the space of random variables is defined which appears to be a kind of a weighted…
In this paper, I use the extension of the excursion set model of Sheth & Tormen (2002) and the barrier shape obtained in Del Popolo & Gambera (1998) to calculate the unconditional halo mass function, and the conditional mass function in…
We present a novel combination of the excursion-set approach with the peak theory formalism in Lagrangian space and provide accurate predictions for halo and void statistics over a wide range of scales. The set-up is based on an effective…
Non-spherical dynamical approximations and models for the gravitational collapse are used to extend the well-known Press \& Schechter (PS) approach, in order to determine analytical expressions for the mass function of cosmic structures.…
The galactic scale challenges of dark matter such as "missing satellite" problem and "too big to fail" problem are the main caveats of standard model of cosmology. These challenges could be solved either by implementing the complicated…
We revisit the derivation of the mass function and the bias of dark matter halos for non-Gaussian initial conditions. We use a steepest-descent approach to point out that exact results can be obtained for the high-mass tail of the halo mass…
The L\'evy walk process for the lower interval of the time of flight distribution ($\alpha<1$) and with finite resting time between consecutive flights is discussed. The motion is restricted to a region bounded by two absorbing barriers and…
The excursion set theory of halo formation is modified by adopting the fractional Brownian motion, to account for possible correlation between merging steps. We worked out analytically the conditional mass function, halo merging rate and…
Structure formation provides a strong test of any cosmic acceleration model because a successful dark energy model must not inhibit {\black or overpredict} the development of observed large-scale structures. Traditional approaches to…
In the Excursion Set approach, halo abundances and clustering are closely related. This relation is exploited in many modern methods which seek to constrain cosmological parameters on the basis of the observed spatial distribution of…
Researching elliptic analogues for equalities and formulas is a new trend in enumerative combinatorics which has followed the previous trend of studying $q$-analogues. Recently Schlosser proposed a lattice path model in the square lattice…
In attempts to explain dark energy, a number of models have been proposed in which the formation of large-scale structure depends on the local environment. These models are highly non-linear and difficult to analyse analytically. N-body…
In this paper we describe the Bayesian link between the cosmological mass function and the distribution of times at which isolated halos of a given mass exist. By assuming that clumps of dark matter undergo monotonic growth on the…
The ConflUent System of Peak trajectories (CUSP) is a rigorous formalism in the framework of the peak theory that allows one to derive from first principles andno free parameters the typical halo properties from the statistics of peaks in…
Motivated by a range of biological applications related to the transport of molecules in cells, we present a modular framework to treat first-passage problems for diffusion in partitioned spaces. The spatial domains can differ with respect…
We present a method, based on the correlation function of excursion sets above a given threshold, to test the Gaussianity of the CMB temperature fluctuations in the sky. In particular, this method can be applied to discriminate between…
Constrained realisations of Gaussian random fields are used in cosmology to design special initial conditions for numerical simulations. We review this approach and its application to density peaks providing several worked-out examples. We…
We obtain exact travelling wave solutions for three families of stochastic one-dimensional nonequilibrium lattice models with open boundaries. These solutions describe the diffusive motion and microscopic structure of (i) of shocks in the…