Related papers: Contact process on a dynamical long range percolat…
We study the contact process in a dynamical random environment defined on the vertices and edges of a graph. For a broad class of processes, we establish an asymptotic shape theorem for the set H_t, which represents the vertices that have…
The quadratic contact process (QCP) is a natural extension of the well studied linear contact process where infected (1) individuals infect susceptible (0) neighbors at rate $\lambda$ and infected individuals recover ($1 \longrightarrow 0$)…
Bootstrap percolation is a process that is used to model the spread of an infection on a given graph. In the model considered here each vertex is equipped with an individual threshold. As soon as the number of infected neighbors exceeds…
A bootstrap percolation process on a graph $G$ is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least $r$ infected neighbours…
The stacked contact process is a stochastic model for the spread of an infection within a population of hosts located on the $d$-dimensional integer lattice. Regardless of whether they are healthy or infected, hosts give birth and die at…
The ordinary contact process is used to model the spread of a disease in a population. In this model, each infected individual waits an exponentially distributed time with parameter 1 before becoming healthy. In this paper, we introduce and…
We introduce the generalized diffusive epidemic process, which is a metapopulation model for an epidemic outbreak where a non-sedentary population of walkers can jump along lattice edges with diffusion rates $D_S$ or $D_I$ if they are…
We consider the contact process on a random graph with fixed degree distribution given by a power law. We follow the work of Chatterjee and Durrett, who showed that for arbitrarily small infection parameter $\lambda$, the survival time of…
This paper is concerned with contact process with random vertex weights on regular trees, and study the asymptotic behavior of the critical infection rate as the degree of the trees increasing to infinity. In this model, the infection…
In this paper we are concerned with contact processes with random edge weights on rooted regular trees. We assign i.i.d weights on each edge on the tree and assume that an infected vertex infects its healthy neighbor at rate proportional to…
The directed last passage percolation (LPP) on the quarter-plane is a growing model. To come into the growing set, a cell needs that the cells on its bottom and on its left to be in the growing set, and then to wait a random time. We…
Graph bootstrap percolation is a discrete-time process capturing the spread of a virus on the edges of $K_n$. Given an initial set $G\subseteq K_n$ of infected edges, the transmission of the virus is governed by a fixed graph $H$: in each…
The regular tree corresponds to the random regular graph as its local limit. For this reason the famous double phase transition of the contact process on regular tree has been seen to correspond to a phase transition on the large random…
Bootstrap percolation is a type of cellular automaton on graphs, introduced as a simple model of the dynamics of ferromagnetism. Vertices in a graph can be in one of two states: `healthy' or `infected' and from an initial configuration of…
Percolation is perhaps the simplest example of a process exhibiting a phase transition and one of the most studied phenomena in statistical physics. The percolation transition is continuous if sites/bonds are occupied independently with the…
Motivated by a model of an area-wide integrated pest management, we develop an interacting particle system evolving in a random environment. It is a generalised contact process in which the birth rate takes two possible values, determined…
In this paper, we study a model of long-range site percolation on graphs of bounded degree, namely the Boolean percolation model. In this model, each vertex of an infinite connected graph is the center of a ball of random radius, and…
Inspired by strict-monotonicity criteria for the time constant in first passage percolation, we investigate convex ordering of point processes in relation to the time constant in first contact percolation. In a nutshell, first contact…
A class of non-local contact processes is introduced and studied using mean-field approximation and numerical simulations. In these processes particles are created at a rate which decays algebraically with the distance from the nearest…
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…