Related papers: Contact processes with random recovery rates and e…
In this paper we are concerned with the SIR (Susceptible-Infective-Removed) epidemic on open clusters of bond percolation on the squared lattice. For the SIR model, a susceptible vertex is infected at rate proportional to the number of…
The basic contact process with parameter $\mu$ altered so that infections of sites that have not been previously infected occur at rate proportional to $\lambda$ instead is considered. Emergence of an infinite epidemic starting out from a…
For two correlated graphs which are independently sub-sampled from a common Erd\H{o}s-R\'enyi graph $\mathbf{G}(n, p)$, we wish to recover their \emph{latent} vertex matching from the observation of these two graphs \emph{without labels}.…
We investigate the role of clustering on the critical behavior of the contact process (CP) on small-world networks using the Watts-Strogatz (WS) network model with an edge rewiring probability p. The critical point is well predicted by a…
Selection bias is a major obstacle toward valid causal inference in epidemiology. Over the past decade, several graphical rules based on causal diagrams have been proposed as the sufficient identification conditions for addressing selection…
We continue the study of renewal contact processes initiated in a companion paper, where we showed that if the tail of the interarrival distribution $\mu$ is heavier than $t^{-\alpha}$ for some $\alpha <1$ (plus auxiliary regularity…
We provide a simple new randomized contraction approach to the global minimum cut problem for simple undirected graphs. The contractions exploit 2-out edge sampling from each vertex rather than the standard uniform edge sampling. We…
The aim of this article is to prove asymptotic shape theorems for the contact process in stationary random environment. These theorems generalize known results for the classical contact process. In particular, if H_t denotes the set of…
Motivated by questions regarding long range percolation, we investigate a non-Markovian analogue of the Harris contact process in $\mathbb{Z}^d$: an individual is attached to each site $x \in \mathbb{Z}^d$, and it can be infected or…
The theme of this paper is the analysis of bootstrap percolation processes on random graphs generated by preferential attachment. This is a class of infection processes where vertices have two states: they are either infected or…
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…
The renewal contact process is a non-Markovian variant of the classical contact process in which recoveries are governed by independent renewal processes with interarrival distribution $\mu$. We establish new sufficient conditions ensuring…
We study both numerically and analytically what happens to a random graph of average connectivity "alpha" when its leaves and their neighbors are removed iteratively up to the point when no leaf remains. The remnant is made of isolated…
We study a model that generalizes the CP with diffusion. An additional transition is included in the model so that at a particular point of its phase diagram a crossover from the directed percolation to the compact directed percolation…
In this paper, we aim at recovering an undirected weighted graph of $N$ vertices from the knowledge of a perturbed version of the eigenspaces of its adjacency matrix $W$. For instance, this situation arises for stationary signals on graphs…
We introduce and study a novel semi-random multigraph process, described as follows. The process starts with an empty graph on $n$ vertices. In every round of the process, one vertex $v$ of the graph is picked uniformly at random and…
We present a randomized algorithm for dynamic graph connectivity. With failure probability less than $1/n^c$ (for any constant $c$ we choose), our solution has worst case running time $O(\log^3 n)$ per edge insertion, $O(\log^4 n)$ per edge…
We consider the statistical inference problem of recovering an unknown perfect matching, hidden in a weighted random graph, by exploiting the information arising from the use of two different distributions for the weights on the edges…
We have studied the phase transition of the contact process near a multiple junction of $M$ semi-infinite chains by Monte Carlo simulations. As opposed to the continuous transitions of the translationally invariant ($M=2$) and semi-infinite…
The contact process is a simple model for the spread of an infection in a structured population. We consider a variant of this process on Bienaym\'e-Galton-Watson trees, where vertices are equipped with a random fitness representing…