Related papers: The Contact Process on Random Graphs and Galton-Wa…
In this paper, we derive a precise estimate for the mean extinction time of the contact process with a fixed infection rate on a star graph with $N$ leaves. Specifically, we determine not only the exponential main factor but also the exact…
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 study degree-penalized contact processes on Galton-Watson trees (GW) and the configuration model. The model we consider is a modification of the usual contact process on a graph. In particular, each vertex can be either infected or…
We study the contact process on a class of geometric random graphs with scale-free degree distribution, defined on a Poisson point process on $\mathbb{R}^d$. This class includes the age-dependent random connection model and the soft Boolean…
We consider the contact process on finite and connected graphs and study the behavior of the extinction time, that is, the amount of time that it takes for the infection to disappear in the process started from full occupancy. We prove,…
In this paper we study the metastability of the contact process on a random regular graph. We show that the extinction time of the contact process, when initialized so that all vertices are infected at time 0, grows exponentially with the…
Branching processes in a random environment are natural generalisations of Galton-Watson processes. In this paper we analyse the asymptotic decay of the survival probability for a sequence of slightly supercritical branching processes in an…
We show that the contact process on the rank-one inhomogeneous random graphs and Erdos-R{\'e}nyi graphs with mean degree large enough survives a time exponential in the size of these graphs for any positive infection rate. In addition, a…
The contact process with an asymptomatic state, introduced in [Belhadji, Lanchier and Mercer, Stochastic Process. Appl., 176:104417, 2024], is a natural variant of the basic contact process that distinguishes between asymptomatic (state 1)…
We study the extinction time $\uptau$ of the contact process on finite trees of bounded degree. We show that, if the infection rate is larger than the critical rate for the contact process on $\Z$, then, uniformly over all trees of degree…
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…
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 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…
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 =…
We consider the contact process on scale-free percolation, a spatial random graph model where the degree distribution of the vertices follows a power law with exponent $\beta$. We study the extinction time $\tau_{G_n}$ of the contact…
We consider the set of random Bienaym\'e-Galton-Watson trees with a bounded number of offspring and bounded number of generations as a statistical mechanics model: a random tree is a rooted subtree of the maximal tree; the spin at a given…
The reproduction speed of a continuous-time branching random walk is proportional to a positive parameter $\lambda$. There is a threshold for $\lambda$, which is called $\lambda_w$, that separates almost sure global extinction from global…
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 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…
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…