Related papers: Functional central limit theorem for the interface…
We study supercritical branching Brownian motion on the real line starting at the origin and with constant drift $c$. At the point $x > 0$, we add an absorbing barrier, i.e.\ individuals touching the barrier are instantly killed without…
In this paper, we introduce a type switching mechanism for the Contact Process on the lattice $\mathbb{Z}^d$. That is, we allow the individual particles/sites to switch between two (or more) types independently of one another, and the…
The binary contact path process (BCPP) introduced in Griffeath (1983) describes the spread of an epidemic on a graph and is an auxiliary model in the study of improving upper bounds of the critical value of the contact process. In this…
The aim of this paper is to study the large population limit of a binary branching particle system with Moran type interactions: we introduce a new model where particles evolve, reproduce and die independently and, with a probability that…
We introduce an interacting particle system which models the inherited sterility method. Individuals evolve on $\mathbb{Z}^d$ according to a contact process with parameter $\lambda>0$. With probability $p \in [0,1]$ an offspring is fertile…
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…
Spreading from a seed is studied by Monte Carlo simulation on a square lattice with two types of sites affecting the rates of birth and death. These systems exhibit a critical transition between survival and extinction. For time- dependent…
We present general results for the contact process by a method which applies to all transitive graphs of bounded degree, including graphs of exponential growth. The model's infection rates are varied through a control parameter, for which…
We consider a discrete-time model for random interface growth which admits exact formulas and converges to the Polynuclear growth model in a particular limit. The height of the interface is initially flat and the evolution involves the…
In this paper we present an individual-based mechanical model that describes the dynamics of two contiguous cell populations with different proliferative and mechanical characteristics. An off-lattice modelling approach is considered…
This paper is focused on a class of spatial birth and death process of the Euclidean space where the birth rate is constant and the death rate of a given point is the shot noise created at its location by the other points of the current…
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…
We study the behaviour of the rightmost occupied site in two models: the Spont process and the contact process with inherited sterility, in dimension 1. Both can be viewed as contact processes evolving in dynamic random environments, where…
We consider the scaling limit of a generic ferromagnetic system with a continuous phase transition, on the half plane with boundary conditions leading to the equilibrium of two different phases below criticality. We use general properties…
We consider the critical behavior at an interface which separates two semi-infinite subsystems belonging to different universality classes, thus having different set of critical exponents, but having a common transition temperature. We…
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 boundary modified contact process models an epidemic spreading in one dimension with two infection parameters, $\lambda_i$ and $\lambda_e$. Starting from a finite infected set, each edge of $\mathbb{Z}$ transmits the infection at rate…
Encounter-based models of diffusion provide a probabilistic framework for analyzing the effects of a partially absorbing reactive surface, in which the probability of absorption depends upon the amount of surface-particle contact time.…
We consider non-colliding Brownian bridges starting from two points and returning to the same position. These positions are chosen such that, in the limit of large number of bridges, the two families of bridges just touch each other forming…
A stochastic comparison result that makes progress towards understanding the classical multitype contact process with unequal death rates is given. It has long been conjectured that the particle type with the largest birth to death rate…