Related papers: The Nonlinear Evolution of Rare Events
We investigate the evolution of non-linear density perturbations by taking into account the effects of deviations from spherical symmetry of a system. Starting from the standard spherical top hat model in which these effects are ignored, we…
We calculate the power spectrum of density fluctuations in the statistical non-equilibrium field theory for classical, microscopic degrees of freedom to first order in the interaction potential. We specialise our result to cosmology by…
Primordial fluctuations in the cosmic density are usually assumed to take the form of a Gaussian random field that evolves under the action of gravitational instability. In the early stages, while they have low amplitude, the fluctuations…
We present an analytical model for the non-spherical collapse of overdense regions out of a Gaussian random field of initial cosmological perturbations. The collapsing region is treated as an ellipsoid of constant density, acted upon by the…
Using the two-point Edgeworth series up to second order we construct the weakly nonlinear conditional probability distribution function for the density field around an overdense region. This requires calculating the two-point analogues of…
I propose a modification of the spherical infall model for the evolution of density fluctuations with initially Gaussian probability distribution and scale-free power spectra. I introduce a generalized form of the initial density…
We investigate the evolution of matter density perturbations within a fractional cosmological framework inspired by fractal space-time constructions in field theory, where a deformation of the integration measure induces non-locality and…
During the evolution of density inhomogeneties in an $\Omega=1$, matter dominated universe, the typical density contrast changes from $\delta\simeq 10^{-4}$ to $\delta\simeq 10^2$. However, during the same time, the typical value of the…
We study the evolution leading to (or regressing from) a large fluctuation in a Statistical Mechanical system. We introduce and study analytically a simple model of many identically and independently distributed microscopic variables $n_m$…
We introduce a schematic non-linear diffusion model where density fluctuations induce a rich out of equilibrium dynamics. The properties of the model are studied by numerical simulations and analytically in a mean field approximation. At…
We generalize the spherical collapse model for the formation of bound objects to apply in a Universe with arbitrary positive cosmological constant. We calculate the critical condition for collapse of an overdense region and give exact…
We calculate the cosmological evolution of the 1-point probability distribution function (PDF), using an analytic approximation that combines gravitational perturbation theory with the Edgeworth expansion of the PDF. Our method applies…
Nonlinear evolution can sometimes be modelled by a deterministic mapping from initial to final of the local smoothed overdensity. Perturbation theory methods base on this deterministic and local mapping and ignore the 'cloud-in-cloud'…
We conduct numerical experiments in which we systematically vary the initial density over four orders of magnitude and the turbulent velocity over a factor ten. In a companion paper, we investigate the dependence of this distribution on the…
Hamilton et al. have suggested an invaluable scaling formula which describes how the power spectra of density fluctuations evolve into the nonlinear regime of hierarchical clustering. This paper presents an extension of their method to…
We investigate the fluctuations around the average density profile in the weakly asymmetric exclusion process with open boundaries in the steady state. We show that these fluctuations are given, in the macroscopic limit, by a centered…
We consider fluctuations of the dissipated energy in nonlinear driven diffusive systems subject to bulk dissipation and boundary driving. With this aim, we extend the recently-introduced macroscopic fluctuation theory to nonlinear driven…
Using a non-perturbative method developed in a previous article (paper II) we investigate the tails of the probability distribution $P(\rho_R)$ of the overdensity within spherical cells. We show that our results for the low-density tail of…
We extend the evolution mapping approach, originally proposed by Sanchez (2022) to describe non-linear matter density fluctuations, to statistics of the cosmic velocity field. This framework classifies cosmological parameters into shape…
This paper investigates whether nonlinear gravitational instability can account for the clustering of galaxies on large and small scales, and for the evolution of clustering with epoch. No CDM-like spectrum is consistent with the shape of…