Related papers: General contact processes: inhomogeneous models, m…
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 ($1 \longrightarrow 0$)…
A little over 25 years ago Pemantle pioneered the study of the contact process on trees, and showed that on homogeneous trees the critical values $\lambda_1$ and $\lambda_2$ for global and local survival were different. He also considered…
Models of random walks are considered in which walkers are born at one location and die at all other locations with uniform death rate. Steady-state distributions of random walkers exhibit dimensionally dependent critical behavior as a…
We study the dynamics of the contact-process, one of the simplest nonequilibrium stochastic processes, taking place on a scale-free network. We consider the network topology as annealed, i.e. all links are rewired at each microscopic time…
We show existence of a non-trivial phase transition for the contact process, a simple model for infection without immunity, on a network which reacts dynamically to the infection trying to prevent an epidemic. This network initially has the…
Molecular dynamics simulations are used to study different definitions of contact at the atomic scale. The roles of temperature, adhesive interactions and atomic structure are studied for simple geometries. An elastic, crystalline substrate…
We introduce the Mass Migration Process (MMP), a conservative particle system on ${\mathbb N}^{{\mathbb Z}^d}$. It consists in jumps of $k$ particles ($k\ge 1$) between sites, with a jump rate depending only on the state of the system at…
We refine previous results concerning the Renewal Contact Processes. We significantly widen the family of distributions for the interarrival times for which the critical value can be shown to be strictly positive. The result now holds for…
A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with $n$ current particles, a new particle is born with instantaneous rate $\lambda_n$ and a particle…
This paper is concerned with a natural variant of the contact process modeling the spread of knowledge on the integer lattice. Each site is characterized by its knowledge, measured by a real number ranging from 0 = ignorant to 1 =…
This paper is concerned with ergodic properties of inhomogeneous Markov processes. Since the transition probabilities depend on initial times, the existing methods to obtain invariant measures for homogeneous Markov processes are not…
We construct matrix product steady state for a class of interacting particle systems where particles do not obey hardcore exclusion, meaning each site can occupy any number of particles subjected to the global conservation of total number…
In this paper, we consider time-inhomogeneous branching processes and time-inhomogeneous birth-and-death processes, in which the offspring distribution and birth and death rates (respectively) vary in time. A classical result of branching…
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…
We study the dynamics of quantum systems interacting with a stream of entangled qubits. Under fairly general conditions, we present a detailed framework describing the conditional dynamical maps for the system, called quantum trajectories,…
We consider a generalized birth-death process (GBDP) whose state space is a finite subset of a $q$-dimensional lattice. It is assumed that there can be a jump of finite step size in all possible directions such that the probability of…
A birth-death-move process with mutations is a Markov model for a system of marked particles in interaction, that move over time, with births and deaths. In addition the mark of each particle may also change, which constitutes a mutation.…
Thermal contact is the archetype of non-equilibrium processes driven by constant non-equilibrium constraints enforced by reservoirs exchanging conserved microscopic quantities. In models with a finite number of possible configurations, if…
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…
An approach to analyse the properties of a particle system is to compare it with different processes to understand when one of them is larger than other ones. The main technique for that is coupling, which may not be easy to construct. We…