Related papers: Tree structure of the percolating Universe
We probe gravitational clustering in N-body simulations using geometrical descriptors sensitive to `connectedness': the genus curve, percolation and shape statistics. We find that both genus and percolation curves provide complementary…
We calculate the average number of critical points of a Gaussian field on a high-dimensional space as a function of their energy and their index. Our results give a complete picture of the organization of critical points and are of…
In this study we explore the cosmological behavior of a non-minimally coupled scalar field that is linked to torsion gravity. We demonstrate the Sorkin-Schutz formalism with general power law teleparallel torsion coupling. The autonomous…
In this paper, we study the level-set of the zero-average Gaussian Free Field on a uniform random $d$-regular graph above an arbitrary level $h\in (-\infty, h_{\star})$, where $h_{\star}$ is the level-set percolation threshold of the GFF on…
Large-scale structures, observed today, are generally believed to have grown from random, small-amplitude inhomogeneities, present in the early Universe. We investigate how gravitational instability drives the distribution of these…
According to the latest evidence, the Universe is entering an era of exponential expansion, where gravitationally bound structures will get disconnected from each other, forming isolated `island universes'. In this scenario, we present a…
The urban networks of London and New York City are investigated as directed graphs within the paradigm of graph percolation. It has been recently observed that urban networks show a critical percolation transition when a fraction of edges…
We show that gravity theories involving disformally transformed metrics in their matter coupling lead to spontaneous growth of various fields in a similar fashion to the spontaneous scalarization scenario in scalar-tensor theories.…
We study (unrooted) random forests on a graph where the probability of a forest is multiplicatively weighted by a parameter $\beta>0$ per edge. This is called the arboreal gas model, and the special case when $\beta=1$ is the uniform forest…
We consider a continuous time random walk on the rooted binary tree of depth $n$ with all transition rates equal to one and study its cover time, namely the time until all vertices of the tree have been visited. We prove that, normalized by…
It is shown that a first-order cosmological perturbation theory for the open, flat and closed Friedmann-Lema\^itre-Robertson-Walker universes admits one, and only one, gauge-invariant variable which describes the perturbation to the energy…
The percolation transitions on hyperbolic lattices are investigated numerically using finite-size scaling methods. The existence of two distinct percolation thresholds is verified. At the lower threshold, an unbounded cluster appears and…
Insight into a number of interesting questions in cosmology can be obtained from the first crossing distributions of physically motivated barriers by random walks with correlated steps. We write the first crossing distribution as a formal…
The explosive percolation problem on the complete graph is investigated via extensive numerical simulations. We obtain the cluster-size distribution at the moment when the cluster size heterogeneity becomes maximum. The distribution is…
We use de Vaucouleurs' power-law density-distance relation, to study a hierarchical perturbation of the Friedmann universe. We solve the Einstein equation and obtain the density contrast and the amplification factor for the perturbation. It…
The methods of conformal field theory are used to compute the crossing probabilities between segments of the boundary of a compact two-dimensional region at the percolation threshold. These probabilities are shown to be invariant not only…
Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some…
The local theory of the critical lines of 2D and 3D Gaussian fields that underline the cosmic structures is presented. In the context of cosmological matter distribution the subset of critical lines of the 3D density field serves to…
Self-similarity and long-range correlations are the remarkable features of the Earth's surface topography. Here we develop an approach based on percolation theory to study the geometrical features of Earth. Our analysis is based on…
We examine the interplay between anisotropy and percolation, i.e., the spontaneous formation of a system spanning cluster in an anisotropic model. We simulate an extension of a benchmark model of continuum percolation, the Boolean model,…