Related papers: The contact process on the regular tree with rando…
We study the contact process on the long-range percolation cluster on $\mathbb{Z}$ where each edge $\langle i,j \rangle$ is open with probability $|i-j|^{-s}$ for $s> 2$. Using a renormalization procedure we apply Peierls-type argument to…
Propagation of contagion in networks depends on the graph topology. This paper is concerned with studying the time-asymptotic behavior of the extended contact processes on static, undirected, finite-size networks. This is a contact process…
We study the behavior of Random Walk in Random Environment (RWRE) on trees in the critical case left open in previous work. Representing the random walk by an electrical network, we assume that the ratios of resistances of neighboring edges…
We investigate the random loop model on the $d$-ary tree. For $d \geq 3$, we establish a (locally) sharp phase transition for the existence of infinite loops. Moreover, we derive rigorous bounds that in principle allow to determine the…
We consider the discrete-time threshold-$\theta \ge 2$ contact process on a random r-regular graph on n vertices. In this process, a vertex with at least \theta occupied neighbors at time t will be occupied at time t+1 with probability p,…
One model of real-life spreading processes is First Passage Percolation (also called SI model) on random graphs. Social interactions often follow bursty patterns, which are usually modelled with i.i.d.~heavy-tailed passage times on edges.…
We performed Monte Carlo simulations of the symbiotic contact process on different spatial dimensions ($d$). On the complete and random graphs (infinite dimension), we observe hysteresis cycles and bistable regions, what is consistent with…
We investigate the contact process on scale-free networks evolving by a stationary dynamics whereby each vertex independently updates its connections with a rate depending on its power. This rate can be slowed down or speeded up by virtue…
In this paper, we derive a precise estimate for the mean extinction time of the contact process with a fixed infection rate on a star graph with $N$ leaves. Specifically, we determine not only the exponential main factor but also the exact…
We investigate the contact process on four different types of scale-free inhomogeneous random graphs evolving according to a stationary dynamics, where each potential edge is updated with a rate depending on the strength of the adjacent…
We study the frog model with death on the biregular tree $\mathbb{T}_{d_1,d_2}$. Initially, there is a random number of awake and sleeping particles located on the vertices of the tree. Each awake particle moves as a discrete-time…
We report on the asymptotic behaviour of a new model of random walk, we term the bindweed model, evolving in a random environment on an infinite multiplexed tree. The term \textit{multiplexed} means that the model can be viewed as a nearest…
We study a contact process running in a random environment in $\mathbb {Z}^d$ where sites flip, independently of each other, between blocking and nonblocking states, and the contact process is restricted to live in the space given by…
We show that the contact process on the rank-one inhomogeneous random graphs and Erdos-R{\'e}nyi graphs with mean degree large enough survives a time exponential in the size of these graphs for any positive infection rate. In addition, a…
Much of the research on the behavior of the SIS model on networks has concerned the infinite size limit; in particular the phase transition between a state where outbreaks can reach a finite fraction of the population, and a state where…
Excitation waves are studied on trees and random networks of coupled active elements. Undamped propagation of such waves is observed in those networks. It represents an excursion from the resting state and a relaxation back to it for each…
Consider a rooted $N$-ary tree. To every vertex of this tree, we attach an i.i.d. continuous random variable. A vertex is called accessible if along its ancestral line, the attached random variables are increasing. We keep accessible…
The shapes of branching trees have been linked to disease transmission patterns. In this paper we use the general Crump-Mode-Jagers branching process to model an outbreak of an infectious disease under mild assumptions. Introducing a new…
The contact process is a stochastic process which exhibits a continuous, absorbing-state phase transition in the Directed Percolation (DP) universality class. In this work, we consider a contact process with a bias in conjunction with an…
We study a contact process (CP) with two species that interact in a symbiotic manner. In our model, each site of a lattice may be vacant or host individuals of species A and/or B; multiple occupancy by the same species is prohibited.…