Related papers: Limitation of the Press-Schechter Formalism
The representation of clouds and associated processes of rain and snow formation remains one of the major uncertainties in climate and weather prediction models. In a companion paper (Part I), we systematically derived a two moment bulk…
K-median and k-means are the two most popular objectives for clustering algorithms. Despite intensive effort, a good understanding of the approximability of these objectives, particularly in $\ell_p$-metrics, remains a major open problem.…
A new way to construct a fitting formula for the halo mass function is presented. Our formula is expressed as a solution to the modified Jedamzik matrix equation that automatically satisfies the normalization constraint. The characteristic…
We present the main results of a numerical study of weak lensing cluster counting. We examine the scaling with cosmology of the projected-density-peak mass function. Our main conclusion is that the projected-peak and the three-dimensional…
This study expands the spontaneous collapse assumptions into the relativistic quantum field theory framework for Dirac fields. By solving Lindblad's master equation using the Keldysh formalism, the effective action is derived, which…
In geometric measure theory, there is interest in studying the interaction of measures with rectifiable sets. Here, we extend a theorem of Badger and Schul in Euclidean space to characterize rectifiable pointwise doubling measures in…
In their seminal paper, Caves and Schumaker presented a new formalism for quantum optics, intended to serve as a building block for describing two-photon processes, in terms of new, generalized qudratures. The important, revolutionary…
We derive cosmological constraints from the probability distribution function (PDF) of evolved large-scale matter density fluctuations. We do this by splitting lines of sight by density based on their count of tracer galaxies, and by…
An analysis of cosmological mixed dark matter models in spatially flat Friedmann Universe with zero $\Lambda$-term is presented. We argue that the introduction of cosmic gravity waves helps to satisfy observational constraints. The analysis…
In this paper, we study the asymptotic behavior of a fully-coupled slow-fast McKean-Vlasov stochastic system. Using the non-linear Poisson equation on Wasserstein space, we first establish the strong convergence in the averaging principle…
The standard definition of particle number fluctuations based on point-like particles neglects the excluded volume effect. This leads to a large and systematic finite-size scaling and an unphysical surface term in the isothermal…
This paper provides, from one side, a review of the theory of the cosmological mass function from a theoretical point of view, starting from the seminal paper of Press & Shechter (1974) to the last developments (Del Popolo & Gambera (1998,…
Based upon the rate equations for the photon distribution function obtained in the previous paper, we study the formal solutions in three different representation forms for the Sunyaev-Zeldovich effect. By expanding the formal solution in…
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…
We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasilinear scales. The Lagrangian theory of gravitational instability of an Einstein-de…
In Polyakov model, a non-perturbative mass gap is formed at leading order semi-classics by instanton effects. By using the notions of critical points at infinity, cluster expansion and Lefschetz thimbles, we show that a third order effect…
We develop a formulation of perturbation theory on spherically symmetric backgrounds based on self-dual curvature equations combined with spherical harmonic expansions. The resulting framework unifies the Regge-Wheeler-Zerilli (RWZ) and…
We analyze within a semiclassical approximation the form factor for the fluctuations of quantum matrix elements around their classical average. We find two contributions: one is proportional to the form factor for the density of states,…
The semiclassical collapse of a homogeneous sphere of dust is studied. After identifying the independent dynamical variables, the system is canonically quantised and coupled equations describing matter (dust) and gravitation are obtained.…
We study the effects of cut-off physics, in the form of a modified algebra inspired by Polymer Quantum Mechanics and by the Generalized Uncertainty Principle representation, on the collapse of a spherical dust cloud. We analyze both the…