Related papers: Sharpness versus robustness of the percolation tra…
Communication networks, power grids, and transportation networks are all examples of networks whose performance depends on reliable connectivity of their underlying network components even in the presence of usual network dynamics due to…
We consider a random walk on top of the contact process on $\mathbb{Z}^d$ with $d\geq 1$. In particular, we focus on the "contact process as seen from the random walk". Under the assumption that the infection rate of the contact process is…
We introduce and solve a model of hardcore particles on a one dimensional periodic lattice which undergoes an active-absorbing state phase transition at finite density. In this model an occupied site is defined to be active if its left…
Bootstrap percolation is an often used model to study the spread of diseases, rumors, and information on sparse random graphs. The percolation process demonstrates a critical value such that the graph is either almost completely affected or…
Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex…
We study two-dimensional critical bootstrap percolation models. We establish that a class of these models including all isotropic threshold rules with a convex symmetric neighbourhood, undergoes a sharp metastability transition. This…
In this paper we are concerned with contact process with random recovery rates on open clusters of bond percolation on $\mathbb{Z}^d$. Let $\xi$ be a positive random variable, then we assigned i. i. d. copies of $\xi$ on the vertices as the…
Consider subcritical Bernoulli bond percolation with fixed parameter p<p_c. We define a dependent site percolation model by the following procedure: for each bond cluster, we colour all vertices in the cluster black with probability r and…
We prove the sharpness of the percolation phase transition for a class of Cox percolation models, i.e., models of continuum percolation in a random environment. The key requirements are that the environment has a finite range of dependence…
Percolation transition is widely observed in networks ranging from biology to engineering. While much attention has been paid to network topologies, studies rarely focus on critical percolation phenomena driven by network dynamics. Using…
We study the percolation in coupled networks with both inner-dependency and inter-dependency links, where the inner- and inter-dependency links represent the dependencies between nodes in the same or different networks, respectively. We…
We study the percolation properties of geometrical clusters defined in the overlap space of two statistically independent replicas of a square-lattice Ising model that are simulated at the same temperature. In particular, we consider two…
In this note we study the phase transition for percolation on quasi-transitive graphs with quasi-transitively inhomogeneous edge-retention probabilities. A quasi-transitive graph is an infinite graph with finitely many different "types" of…
When a finite volume of an etching solution comes in contact with a disordered solid, a complex dynamics of the solid-solution interface develops. Since only the weak parts are corroded, the solid surface hardens progressively. If the…
We derive a sufficient condition for the existence of a subcritical percolation phase for a wide range of continuum percolation models where each vertex is embedded into Euclidean space according to an iid-marked stationary Poisson point…
We are interested in phase transitions in certain percolation models on point processes and their dependence on clustering properties of the point processes. We show that point processes with smaller void probabilities and factorial moment…
The critical behavior of the contact process in disordered and periodic binary 2d-lattices is investigated numerically by means of Monte Carlo simulations as well as via an analytical approximation and standard mean field theory.…
We study critical spreading in a surface-modified directed percolation model in which the left- and right-most sites have different occupation probabilities than in the bulk. As we vary the probability for growth at an edge, the critical…
We consider an inhomogeneous oriented percolation model introduced by de Lima, Rolla and Valesin. In this model, the underlying graph is an oriented rooted tree in which each vertex points to each of its $d$ children with `short' edges, and…
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…