Related papers: The Contact Process with Switching
The contact process is a particular case of birth-and-death processes on infinite particle configurations. We consider the contact models on locally compact separable metric spaces. We prove the existence of a one-parameter set of invariant…
Bezuidenhout and Grimmett proved that the critical contact process dies out. Here, we generalize the result to the so called contact process in a random evolving environment (CPREE), introduced by Erik Broman. This process is a…
We study the limiting behavior of an interacting particle system evolving on the lattice $Z^{d}$ for $d\ge 3$. The model is known as the contact process with rapid stirring. The process starts with a single particle at the origin. Each…
We introduce and study the mutating contact process, a variant of the multitype contact process, where one type mutates at a constant rate to the other type. We prove that on $\mathbb{Z}$ a single mutant cannot survive while on…
We consider the contact process on a dynamic graph defined as a random $d$-regular graph with a stationary edge-switching dynamics. In this graph dynamics, independently of the contact process state, each pair $\{e_1,e_2\}$ of edges of 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…
Motivated by recent findings, we discuss the existence of a direct and robust mechanism providing discontinuous absorbing transitions in short range systems with single species, with no extra symmetries or conservation laws. We consider…
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 study two one-dimensional variants of the contact process: the contact-and-barrier process, where the population evolves in a region delimited by a randomly moving barrier, and the multitype contact process, in which two species compete…
Switching interacting particle systems studied in probability theory are the stochastic processes of hopping particles on a lattice made up of slow and fast particles, where the switching between these types of particles occurs randomly at…
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 ($1 \longrightarrow 0$)…
We study the phase transition phenomena for long-range oriented percolation and contact process. We studied a contact process in which the range of each vertex are independent, updated dynamically and given by some distribution $N$. We also…
We consider spin systems on $\Z$ (i.e.\ interacting particle systems on $\Z$ in which each coordinate only has two possible values and only one coordinate changes in each transition) whose rates are determined by another process, called a…
In this paper we are concerned with the two-stage contact process introduced in \cite{Krone1999} on a high-dimensional lattice. By comparing this process with an auxiliary model which is a linear system, we obtain two limit theorems for…
We consider a contact process on $Z^d$ with two species that interact in a symbiotic manner. Each site can either be vacant or occupied by individuals of species $A$ and/or $B$. Multiple occupancy by the same species at a single site is…
It is known that the limiting behavior of the contact process strongly depends upon the geometry of the graph on which particles evolve: while the contact process on the regular lattice exhibits only two phases, the process on homogeneous…
Contact processes describe the transmission of distinct properties of nodes via the links of a network. They provide a simple framework for many phenomena, such as epidemic spreading and opinion formation. Combining contact processes with…
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…
The contact process is a simple model for the spread of an infection in a structured population. We investigate the case when the underlying structure evolves dynamically as a degree-dependent dynamical percolation model. Starting with a…
In this paper we are concerned with the two-stage contact process on the lattice $\mathbb{Z}^d$ introduced in \cite{Krone1999}. We gives a limit theorem of the critical infection rate of the process as the dimension $d$ of the lattice grows…