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Network geometry has strong effects on network dynamics. In particular, the underlying hyperbolic geometry of discrete manifolds has recently been shown to affect their critical percolation properties. Here we investigate the properties of…
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…
One of the most impressive features of continuous phase transitions is the concept of universality, that allows to group the great variety of different critical phenomena into a small number of universality classes. All systems belonging to…
The nonequilibrium phase transition in a system of diffusing, coagulating particles in the presence of a steady input and evaporation of particles is studied. The system undergoes a transition from a phase in which the average number of…
In this chapter of the e-book "Self-Organized Criticality Systems" we summarize some theoretical approaches to self-organized criticality (SOC) phenomena that involve percolation as an essential key ingredient. Scaling arguments, random…
Percolation offers acknowledged models of random media when the relevant medium characteristics can be described as a binary feature. However, when considering habitat modeling in ecology, a natural constraint comes from nearest-neighbor…
We report the discovery of a discrete hierarchy of micro-transitions occurring in models of continuous and discontinuous percolation. The precursory micro-transitions allow us to target almost deterministically the location of the…
We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the…
We generate point configurations (PCs) by thresholding the local energy of the Ashkin-Teller model in two dimensions (2D) and study the percolation transition at different values of $\lambda$ along the critical Baxter line by varying the…
We investigate continuum percolation for Cox point processes, that is, Poisson point processes driven by random intensity measures. First, we derive sufficient conditions for the existence of non-trivial sub- and super-critical percolation…
Stochastic point processes relevant to the theory of long-range aperiodic order are considered that display diffraction spectra of mixed type, with special emphasis on explicitly computable cases together with a unified approach of…
The localization transition and the critical properties of the Lorentz model in three dimensions are investigated by computer simulations. We give a coherent and quantitative explanation of the dynamics in terms of continuum percolation…
Universal behavior is a typical emergent feature of critical systems. A paramount model of the non-equilibrium critical behavior is the directed bond percolation process that exhibits an active- to-absorbing state phase transition in the…
Machine learning for phase transition has received intensive research interest in recent years. However, its application in percolation still remains challenging. We propose an auxiliary Ising mapping method for machine learning study of…
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…
Hybrid percolation transitions (HPTs) induced by cascading processes have been observed in diverse complex systems such as $k$-core percolation, breakdown on interdependent networks and cooperative epidemic spreading models. Much effort has…
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 study the effects of spatially inhomogeneous diffusion on the non-equilibrium phase transition in the contact process. The directed-percolation critical point in the contact process is known to be stable against the addition of a…
Discontinuous percolation transitions and the associated tricritical points are manifest in a wide range of both equilibrium and non-equilibrium cooperative phenomena. To demonstrate this, we present and relate the continuous and first…
A substantial share of the Earth's land surface is managed by humans, with cities representing the most extreme form of anthropogenic land use. There are zillion ways in which settlements can be arranged across a given area, and their…