相关论文: Unusual properties of contact processes on percola…
We construct graphs (trees of bounded degree) on which the contact process has critical rate (which will be the same for both global and local survival) equal to any prescribed value between zero and $\lambda_c(\mathbb{Z})$, the critical…
We study the phase diagram and critical behavior of the one-dimensional pair contact process (PCP) with a particle source using cluster approximations and extensive simulations. The source creates isolated particles only, not pairs, and so…
In this paper, we prove lower and upper bounds for the extinction time of the contact process on random geometric graphs with connecting radius tending to infinity. We obtain that for any infection rate $\lambda >0$, the contact process on…
We consider the discrete Boolean model of percolation on graphs satisfying a doubling metric condition. We study sufficient conditions on the distribution of the radii of balls placed at the points of a Bernoulli point process for the…
We present quasi-stationary simulations of the two-dimensional contact process with quenched disorder included through the random dilution of a fraction of the lattice sites (these sites are not susceptible to infection). Our results…
In graph bootstrap percolation, edges of an Erd\H{o}s-R\'enyi random graph ${\mathcal G}_{n,p}$ are initially active. Activation spreads to other edges of the complete graph $K_n$ by an iterative process governed by a fixed graph $H$,…
We study a model that generalizes the CP with diffusion. An additional transition is included in the model so that at a particular point of its phase diagram a crossover from the directed percolation to the compact directed percolation…
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…
In this paper we introduce a contact process in an evolving random environment (CPERE) on a connected and transitive graph with bounded degree, where we assume that this environment is described through an ergodic spin systems with finite…
We argue that the unscreened Coulomb interaction in graphene provides a positive, universal, and logarithmic correction to scaling of zero-temperature conductivity with frequency. The combined effect of the disorder due to wrinkling of the…
We study the connectivity of random subgraphs of the $d$-dimensional Hamming graph $H(d, n)$, which is the Cartesian product of $d$ complete graphs on $n$ vertices. We sample the random subgraph with an i.i.d.\ Bernoulli bond percolation on…
Exclusion processes became paradigmatic models of nonequilibrium interacting particle systems of wide range applicability both across the natural and the applied, social and technological sciences. Usually they are defined as a…
We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…
In this paper we study the metastability of the contact process on a random regular graph. We show that the extinction time of the contact process, when initialized so that all vertices are infected at time 0, grows exponentially with the…
We study percolation properties of the upper invariant measure of the contact process on $\mathbb{Z}^d$. Our main result is a sharp percolation phase transition with exponentially small clusters throughout the subcritical regime and a…
The conductance through a quantum point contact created by a sharp and hard metal tip on the graphite surface has features which to our knowledge have not been encountered so far in metal contacts or in nanowires. In this paper we first…
Let a random geometric graph be defined in the supercritical regime for the existence of a unique infinite connected component in Euclidean space. Consider the first-passage percolation model with independent and identically distributed…
We study the contact process on random graphs with low infection rate $\lambda$. For random $d$-regular graphs, it is known that the survival time is $O(\log n)$ below the critical $\lambda_c$. By contrast, on the Erd\H{o}s-R\'enyi random…
Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…
The secrecy graph is a random geometric graph which is intended to model the connectivity of wireless networks under secrecy constraints. Directed edges in the graph are present whenever a node can talk to another node securely in the…