Related papers: On the One-Dimensional Contact Process with Enhanc…
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…
We prove the continuity of the shape governing the asymptotic growth of the supercritical contact process in Z^d , with respect to the infection parameter. The proof is valid in any dimension d $\ge$ 1.
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 contact process on a random bipartite connection hypergraph generated from two Poisson point processes, with mark-dependent connection thresholds. For asymmetric infection rates and asymmetric power law tail decays of the two…
In this work we use the technique of the partial differential approximants to determine, from a pertubative supercritical series expansion for the ulimate survival probability, the critical line of the contact process model in one dimension…
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 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…
We study the threshold $\theta$ contact process on $\mathbb{Z}^d$ with infection parameter $\lambda$. We show that the critical point $\lambda_{\mathrm{c}}$, defined as the threshold for survival starting from every site occupied, vanishes…
We construct graphs (trees of bounded degree) on which the contact process has critical rate (which will be the same for both global and local survival) equal to any prescribed value between zero and $\lambda_c(\mathbb{Z})$, the critical…
We investigate a non-Markovian analogue of the Harris contact process in a finite connected graph G=(V,E): an individual is attached to each site x in V, and it can be infected or healthy; the infection propagates to healthy neighbors just…
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…
We consider the contact process near an extended surface defect, where the local control parameter deviates from the bulk one by an amount of $\lambda(l)-\lambda(\infty) = A l^{-s}$, $l$ being the distance from the surface. We concentrate…
We study a two dimensional version of Neuhauser's long range sexual reproduction model and prove results that give bounds on the critical values $\lambda_f$ for the process to survive from a finite set and $\lambda_e$ for the existence of a…
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…
We introduce a method to prove metastability of the contact process on Erd\H{o}s-R\'enyi graphs and on configuration model graphs. The method relies on uniformly bounding the total infection rate from below, over all sets with a fixed…
We study survival and extinction of a long-range infection process on a diluted one-dimensional lattice in discrete time. The infection can spread to distant vertices according to a Pareto distribution, however spreading is also prohibited…
What is the long-time behavior of the law of a contact process started with a single infected site, distributed according to counting measure on the lattice? This question is related to the configuration as seen from a typical infected site…
We study critical spreading dynamics in the two-dimensional contact process (CP) with quenched disorder in the form of random dilution. In the pure model, spreading from a single particle at the critical point $\lambda_c$ is characterized…
We consider the contact process on a countable-infinite and connected graph of bounded degree. For this process started from the upper invariant measure, we prove certain uniform mixing properties under the assumption that the infection…
The contact process is a simple infection spreading model showcasing an out-of-equilibrium phase transition between a macroscopically active and an inactive phase. Such absorbing state phase transitions are often sensitive to the presence…