Related papers: Modelling the evolution of correlation functions i…
We consider the Rosenzweig-Porter model of random matrix which interpolates between Poisson and gaussian unitary statistics and compute exactly the two-point correlation function. Asymptotic formulas for this function are given near the…
We show how, based on considerations on the observed form of the galaxy 2-point spatial correlation function xi(r), a very simplified -- yet surprisingly effective -- model for the linear density fluctuations power spectrum can be…
The correlation function xi(r) of matter in the non-linear regime is assumed to be determined by the density profiles rho(r) and the mass distribution n(M) of virialized halos. The Press--Schechter approach is used to compute n(M), and the…
Many statistics available to constrain non-Gaussianity from inflation are simplest to use under the assumption that the curvature correlation functions are hierarchical. That is, if the n-point function is proportional to the (n-1) power of…
In order to characterise non-equilibrium growth processes, we study the behaviour of global quantities that depend in a non-trivial way on two different times. We discuss the dynamical scaling forms of global correlation and response…
N-Point Correlation Functions, usually with N = 2, 3, and their Fourier-space analogs power spectrum and bispectrum, are major tools used in cosmology to capture the clustering of large-scale structure. We outline how the clustering these…
Future large scale structure surveys will provide increasingly tight constraints on our cosmological model. These surveys will report results on the distance scale and growth rate of perturbations through measurements of Baryon Acoustic…
Context: Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used in Bayesian parameter estimation, their likelihood function is usually replaced by a Gaussian approximation.…
We consider the long-standing problem of predicting the hierarchical clustering amplitudes $S_p$ in the strongly non-linear regime of gravitational evolution. N-body results for the non-linear evolution of the bispectrum (the Fourier…
In the gravitational evolution of a cold infinite particle distribution, two-body interactions can be predominant at early times: we show that, by treating the simple case of a Poisson particle distribution in a static universe as an…
We study the interplay of clumping at small scales with the collapse and relaxation of perturbations at larger scales using N-Body simulations. We quantify the effect of collapsed haloes on perturbations at larger scales using two point…
We consider nonlinear biasing models of galaxies with particular attention to a correlation between linear and quadratic biasing coefficients, b_1 and b_2. We first derive perturbative expressions for b_1 and b_2 in halo and peak biasing…
We study the density of specular reflection points in the geometrical optics limit when light scatters off fluctuating interfaces and membranes in thermodynamic equilibrium. We focus on the statistical mechanics of both capillary-gravity…
Much of interesting complex biological behaviour arises from collective properties. Important information about collective behaviour lies in the time and space structure of fluctuations around average properties, and two-point correlation…
We use a recently derived diagrammatic formulation of the dynamics of interacting Brownian particles [G. Szamel, J. Chem. Phys. 127, 084515 (2007)] to study a four-point dynamic density correlation function. We re-sum a class of diagrams…
Several recent studies have shown how to properly calculate the observed clustering of galaxies in a relativistic context, and uncovered corrections to the Newtonian calculation that become significant on scales near the horizon. Here, we…
We describe various expansion schemes that can be used to study gravitational clustering. Obtained from the equations of motion or their path-integral formulation, they provide several perturbative expansions that are organized in different…
When analyzing experimental or simulation time-series data, the question arises whether it is possible to tell from a one-dimensional time-dependent trajectory whether the system is in equilibrium or not. We here consider the…
We developed the functional form of the two-point correlation function under the approximation of fixed particle number density n(bar). We solved the quasi-linear partial differential equation (PDE) through the method of characteristics to…
We investigate consistency relations for non-Gaussianity. We provide a model-independent dynamical proof for the consistency relation of 3-point correlation functions from the Hamiltonian and field redefinition. This relation can be applied…