Related papers: Percolation-like behavior of some optimal coalitio…
The site percolation on the triangular lattice stands out as one of the few exactly solved statistical systems. By initially configuring critical percolation clusters of this model and randomly reassigning the color of each percolation…
Universality is a fundamental concept in modern physics. For the $q$-state Potts model, the critical exponents are merely determined by the order-parameter symmetry $S_q$, spatial dimensionality and interaction range, independent of…
Modeling how networks change under structural perturbations can yield foundational insights into network robustness, which is critical in many real-world applications. The largest connected component is a popular measure of network…
We introduce a nonequilibrium percolation model which shows a self-organized critical (SOC) state and several periodic states. In the SOC state, the correlation length diverges slower than the system size, and the corresponding exponent…
Human development has far-reaching impacts on the surface of the globe. The transformation of natural land cover occurs in different forms and urban growth is one of the most eminent transformative processes. We analyze global land cover…
We study inhomogeneous Bernoulli bond percolation on the graph $G \times \mathbb{Z}$, where $G$ is a connected quasi-transitive graph. The inhomogeneity is introduced through a random region $R$ around the origin axis…
The existence (or not) of infinite clusters is explored for two stochastic models of intersecting line segments in $d \ge 2$ dimensions. Salient features of the phase diagram are established in each case. The models are based on site…
We present an exact solution of percolation in a generalized class of Watts-Strogatz graphs defined on a 1-dimensional underlying lattice. We find a non-classical critical point in the limit of the number of long-range bonds in the system…
We propose a model of mobile agents to construct social networks, based on a system of moving particles by keeping track of the collisions during their permanence in the system. We reproduce not only the degree distribution, clustering…
We describe deformations of non-linear (birational) representations of discrete groups generated by involutions, having their origin in the theory of the symmetric five-state Potts model. One of the deformation parameters can be seen as the…
We investigate how knowledge percolates and clusters in a given knowledge space. We introduce a simple model of knowledge organization in which each contribution spans a certain number of items. If this contribution overlaps with others…
Quantum networks are natural scenarios for the communication of information among distributed parties, and the arena of promising schemes for distributed quantum computation. Measurement-based quantum computing is a prominent example of how…
The social networks that infectious diseases spread along are typically clustered. Because of the close relation between percolation and epidemic spread, the behavior of percolation in such networks gives insight into infectious disease…
In the last years the Prisoner Dilemma (PD) has become a paradigm for the study of the emergence of cooperation in spatially structured populations. Such structure is usually assumed to be given by a graph. In general, the success of…
We use molecular dynamics simulations to study a model of the gelation transition with a dynamic bond forming procedure. After establishing evidence for 3D percolation as the static universality class, we turn our attention to the dynamics…
Universality in the behavior of complex systems often reveals itself in the form of scale-invariant distributions that are essentially independent of the details of the microscopic dynamics. A representative paradigm of complex behavior in…
Herein, we propose a site random cluster model by introducing an additional cluster weight in the partition function of the traditional site percolation. To simulate the model on a square lattice, we combine the color-assignation and the…
We consider robustness and percolation properties of the networks of networks, in which random nodes in different individual networks (layers) can be interdependent. We explore the emergence of the giant mutually connected component,…
Statistical physicists have become interested in models of collective social behavior such as opinion formation, where individuals change their inherently preferred opinion if their friends disagree. Real preferences often depend on…
We apply percolation theory to a recently proposed measure of fragmentation $F$ for social networks. The measure $F$ is defined as the ratio between the number of pairs of nodes that are not connected in the fragmented network after…