Related papers: On some threshold-one attractive interacting parti…

We consider continuous-time consensus seeking systems whose time-dependent interactions are cut-balanced, in the following sense: if a group of agents influences the remaining ones, the former group is also influenced by the remaining ones…

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…

In this paper we are concerned with bias voter models on trees and lattices, where the vertex in state 0 reconsiders its opinion at a larger rate than that of the vertex in state 1. For the process on tree with product measure as initial…

We study one specific version of the contact process on a graph. Here, we allow multiple infections carried by the nodes and include a probability of removing nodes in a graph. The removal probability is purely determined by the number of…

We consider a class of multi-type particle systems having similar structure to the contact process and show that additivity is equivalent to the existence of a dual process, extending a result of Harris. We give two additional…

In the multitype contact process, vertices of a graph can be empty or occupied by a type 1 or a type 2 individual; an individual of type $i$ dies with rate 1 and sends a descendant to a neighboring empty site with rate $\lambda_i$. We study…

We study the supercritical contact process on Galton-Watson trees and periodic trees. We prove that if the contact process survives weakly then it dominates a supercritical Crump-Mode-Jagers branching process. Hence the number of infected…

Consider the following stochastic model for immune response. Each pathogen gives birth to a new pathogen at rate $\lambda$. When a new pathogen is born, it has the same type as its parent with probability $1 - r$. With probability $r$, a…

We examine an interacting particle system on trees commonly referred to as the frog model. For its initial state, it begins with a single active particle at the root and i.i.d. $\mathrm{Poiss}(\lambda)$ many inactive particles at each…

A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are…

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…

A tree $T$ is said to be homogeneous if it is uniquely rooted and there exists an integer $b\meg 2$, called the branching number of $T$, such that every $t\in T$ has exactly $b$ immediate successors. A vector homogeneous tree $\mathbf{T}$…

We study the voter model, under node and link update, and the related invasion process on a single strongly connected component of a directed network. We implement an analytical treatment in the thermodynamic limit using the heterogeneous…

The q-voter model is a spin-flip system in which the rate of flipping to type i is given by the qth power of the proportion of nearest neighbours in type i for $i=0,1$. If $q=1$ it reduces to the classical voter model. We show that in the…

We consider a class of reinforcement processes, called WARMs, on tree graphs. These processes involve a parameter $\alpha$ which governs the strength of the reinforcement, and a collection of Poisson processes indexed by the vertices of the…

We study a system of simple random walks on $\mathcal{T}_{d,n} = \mathcal{V}_{d,n}, \mathcal{E}_{d,n})$, the $d$-ary tree of depth $n$, known as the frog model. Initially there are Pois($\lambda$) particles at each site, independently, with…

We consider the dynamics of a population spatially structured in colonies that are vulnerable to catastrophic events occurring at random times, which randomly reduce their population size and compel survivors to disperse to neighboring…

We analyze the properties of the contact process with long-range interactions by the use of a kinetic ensemble in which the total number of particles is strictly conserved. In this ensemble, both annihilation and creation processes are…

We give a construction of a tree in which the contact process with any positive infection rate survives but, if a certain privileged edge $e^*$ is removed, one obtains two subtrees in which the contact process with infection rate smaller…

We study the ergodic theory of a multitype contact process with equal death rates and unequal birth rates on the $d$-dimensional integer lattice and regular trees. We prove that for birth rates in a certain interval there is coexistence on…