Related papers: Homological Percolation and the Euler Characterist…
We consider percolation in a multiscale Boolean model. This model is defined as the union of scaled independent copies of a given Boolean model. The scale factor of the $n^{\textrm{th}}$ copy is $\rho^{-n}$. We prove, under optimal…
Percolation theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the…
The basic notion of percolation in physics assumes the emergence of a giant connected (percolation) cluster in a large disordered system when the density of connections exceeds some critical value. Until recently, the percolation phase…
We study bond percolation for a family of infinite hyperbolic graphs. We relate percolation to the appearance of homology in finite versions of these graphs. As a consequence, we derive an upper bound on the critical probabilities of the…
We provide a simple proof that graphs in a general class of self-similar networks have zero percolation threshold. The considered self-similar networks include random scale-free graphs with given expected node degrees and zero clustering,…
Correlations are known to play a crucial role in determining the structure of complex networks. Here we study how their presence affects the computation of the percolation threshold in random hypergraphs. In order to mimic the correlation…
We propose a real-space formalism of the topological Euler class, which characterizes the fragile topology of two-dimensional systems with real wave functions. This real-space description is characterized by local Euler markers whose…
We study Lauricella's hypergeometric function F_C by using twisted (co)homology groups. We construct twisted cycles with respect to an Euler-type integral representation of F_C. These cycles correspond to 2^m linearly independent solutions…
We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks…
The continuum percolation for Markov (or Gibbs) germ-grain models is investigated. The grains are assumed circular with random radii on a compact support. The morphological interaction is the so-called Quermass interaction defined by a…
Bootstrap percolation on a graph iteratively enlarges a set of occupied sites by adjoining points with at least $\theta$ occupied neighbors. The initially occupied set is random, given by a uniform product measure, and we say that spanning…
Hyperuniform structures are disordered, correlated systems in which density fluctuations are suppressed at large scales. Such a property generalizes the concept of order in patterns and is relevant across diverse physical systems. We…
For binary fluid mixtures of spherical particles in which the two species are sufficiently different in size, the dominant wavelength of oscillations of the pair correlation functions is predicted to change from roughly the diameter of the…
The Hamming torus of dimension $d$ is the graph with vertices $\{1,\dots,n\}^d$ and an edge between any two vertices that differ in a single coordinate. Bootstrap percolation with threshold $\theta$ starts with a random set of open…
General conservation equations are derived for 2D dense granular flows from the Euler equation within the Boussinesq approximation. In steady flows, the 2D fields of granular temperature, vorticity and stream function are shown to be…
Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…
Porous media are often modelled as systems of overlapping obstacles, which leads to the problem of two percolation thresholds in such systems, one for the porous matrix and the other one for the void space. Here we investigate these…
Percolation is a cornerstone concept in physics, providing crucial insights into critical phenomena and phase transitions. In this study, we adopt a kinetic perspective to reveal the scaling behaviors of higher-order gaps in the largest…
We study the limiting behavior of the zeros of the Euler polynomials. When linearly scaled, they approach a definite curve in the complex plane related to the Szego curve which governs the behavior of the roots of the Taylor polynomials…
We use holography to study the dynamics of a strongly-coupled gauge theory in four-dimensional de Sitter space with Hubble rate $H$. The gauge theory is non-conformal with a characteristic mass scale $M$. We solve Einstein's equations…