Related papers: Tree structure of the percolating Universe
Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount…
In this work we demonstrate the ability of the Minimal Spanning Tree to duplicate the information contained within a percolation analysis for a point dataset. We show how to construct the percolation properties from the Minimal Spanning…
Using percolation statistics we, for the first time, demonstrate the universal character of a network pattern in the real space, mass distributions resulting from nonlinear gravitational instability of initial Gaussian fluctuations.…
For the Gaussian free field on a $(d + 1)$-regular tree with $d \geq 2$, we study the percolative properties of its level sets in the critical and the near-critical regime. In particular, we show the continuity of the percolation…
An attractive and simple hypothesis for the formation of large-scale structure is that it developed by gravitational instability from primordial fluctuations with an initially Gaussian probability distribution. Non-linear gravitational…
Suspensions of hard core spherical particles of diameter $D$ with inter-core connectivity range $\delta$ can be described in terms of random geometric graphs, where nodes represent the sphere centers and edges are assigned to any two…
Numerical simulations and observations show that galaxies are not uniformly distributed. In cosmology, the largest known structures in the universe are galaxy filaments formed from the hierarchical clustering of galaxies due to…
We study intersection properties of two or more independent tree-like random graphs. Our setting encompasses critical, possibly long range, Bernoulli percolation clusters, incipient infinite clusters, as well as critical branching random…
The nature of level set percolation in the two-dimension Gaussian Free Field has been an elusive question. Using a loop-model mapping, we show that there is a nontrivial percolation transition, and characterize the critical point. In…
We investigate level-set percolation of the Gaussian free field on transient trees, for instance on super-critical Galton-Watson trees conditioned on non-extinction. Recently developed Dynkin-type isomorphism theorems provide a comparison…
We study topological properties of large scale structure in a set of scale free N-body simulations using the genus and percolation curves as topological characteristics. Our results show that as gravitational clustering advances, the…
We show by extensive simulations that the whole supercritical phase of the three-dimensional uniform forest model simultaneously exhibits an infinite tree and a rich variety of critical phenomena. Besides typical scalings like algebraically…
The formalism to compute the geometrical and topological one-point statistics of mildly non-Gaussian 2D and 3D cosmological fields is developed. Leveraging the isotropy of the target statistics, the Gram-Charlier expansion is reformulated…
The problem of solving perturbatively the equations describing the evolution of self-gravitating collisionless matter in an expanding universe considerably simplifies when directly formulated in terms of the gravitational and velocity…
While the universe becomes more and more homogeneous at large scales, statistical analysis of galaxy catalogs have revealed a fractal structure at small-scales (\lambda < 100 h^{-1} Mpc), with a fractal dimension D=1.5-2 (Sylos Labini et al…
We present a unifying, consistent, finite-size-scaling picture for percolation theory bringing it into the framework of a general, renormalization-group-based, scaling scheme for systems above their upper critical dimensions $d_c$.…
Gravity is a non-linear theory, and hence, barring cancellations, the initial super-horizon perturbations produced by inflation must contain some minimum amount of mode coupling, or primordial non-Gaussianity. In single-field slow-roll…
We study the trajectory of a simple random walk on a d-regular graph with d>2 and locally tree-like structure as the number n of vertices grows. Examples of such graphs include random d-regular graphs and large girth expanders. For these…
We consider the Gaussian free field on two-dimensional slabs with a thickness described by a height $h$ at spatial scale $N$. We investigate the radius of critical clusters for the associated cable-graph percolation problem, which depends…
Models of percolation processes on networks currently assume locally tree-like structures at low densities, and are derived exactly only in the thermodynamic limit. Finite size effects and the presence of short loops in real systems however…