Related papers: Tree structure of the percolating Universe

We study percolation as a critical phenomenon on a multifractal support. The scaling exponents of the the infinite cluster size ($\beta$ exponent) and the fractal dimension of the percolation cluster ($d_f$) are quantities that seem do not…

We calculate the strength of the tidal field produced by the large-scale density field acting on primordial density perturbations in power law models. By analysing changes in the orientation of the deformation tensor, resulted from…

We present a new approach to model the gravitational dynamics of large-scale structures. Instead of solving the equations of motion up to a finite perturbative order or building phenomenological models, we follow the evolution of the…

We describe a percolation problem on lattices (graphs, networks), with edge weights drawn from disorder distributions that allow for weights (or distances) of either sign, i.e. including negative weights. We are interested whether there are…

We consider the lattice version of the free field in two dimensions and study the fractal structure of the sets where the field is unusually high (or low). We then extend some of our computations to the case of the free field conditioned on…

Supersymmetric vacua (`universes') of string/M theory may be identified with certain critical points of a holomorphic section (the `superpotential') of a Hermitian holomorphic line bundle over a complex manifold. An important physical…

We study structure formation in a set of cosmological simulations to uncover the scales in the initial density field that gave rise to the formation of present-day structures. Our simulations share a common primordial power spectrum (here…

This is the first paper of a series of two devoted to develop a practical method to describe the growth history of bound virialized objects in the gravitational instability scenario without resorting to $N$-body simulations. Here we present…

The matter density field exhibits a nearly lognormal probability density distribution (PDF) after entering into the nonlinear regime. Recently, it has been shown that the shape of the power spectrum of a logarithmically transformed density…

In the context of percolation in a regular tree, we study the size of the largest cluster and the length of the longest run starting within the first d generations. As d tends to infinity, we prove almost sure and weak convergence results.

We study bootstrap percolation with the threshold parameter $\theta \geq 2$ and the initial probability $p$ on infinite periodic trees that are defined as follows. Each node of a tree has degree selected from a finite predefined set of…

We present new perturbation theory (PT) predictions in the Spherical Collapse (SC) model for the 2-point moments of the large-scale distribution of dark matter density in the universe. We assume that these fluctuations grow under gravity…

We consider the model of random trees introduced by Devroye (1999), the so-called random split trees. The model encompasses many important randomized algorithms and data structures. We then perform supercritical Bernoulli bond-percolation…

We outline the physical picture of the high-redshift Ly-alpha forest that has emerged from cosmological simulations, describe statistical characteristics of the forest that can be used to test theories of structure formation, present a…

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…

We define a continuum percolation model that provides a collection of random ellipses on the plane and study the behavior of the covered set and the vacant set, the one obtained by removing all ellipses. Our model generalizes a construction…

We consider the behaviour of a critical system in the presence of a gradient perturbation of the couplings. In the direction of the gradient an interface region separates the ordered phase from the disordered one. We develop a scaling…

We investigate the morphological properties of large-scale structure in the Universe and the physical processes that modify the excursion-set morphology of the three-dimensional matter density field. Using the Quijote N-body simulation…

I analyze the density perturbations in a cosmological model with a scalar field coupled to ordinary matter, such as one obtains in string theory and in conformally transformed scalar-tensor theories. The spectrum of multipoles on the last…

In invasion percolation, the edges of successively maximal weight (the outlets) divide the invasion cluster into a chain of ponds separated by outlets. On the regular tree, the ponds are shown to grow exponentially, with law of large…