Related papers: A Metastability Result for the Contact Process on …
We show that the critical value for the contact process on a vertex-transitive graph G with finitely many edges added and/or removed is the same as the critical value for the contact process on G.
We study the condensation regime of the finite reversible inclusion process, i.e., the inclusion process on a finite graph $S$ with an underlying random walk that admits a reversible measure. We assume that the random walk kernel is…
We consider the averaging process on a graph, that is the evolution of a mass distribution undergoing repeated averages along the edges of the graph at the arrival times of independent Poisson processes. We establish cutoff phenomena for…
The susceptible--infected--susceptible (SIS) epidemic process on complex networks can show metastability, resembling an endemic equilibrium. In a general setting, the metastable state may involve a large portion of the network, or it can be…
Coarsening of sand ripples is studied in a one-dimensional stochastic model, where neighboring ripples exchange mass with algebraic rates, $\Gamma(m) \sim m^\gamma$, and ripples of zero mass are removed from the system. For $\gamma < 0$…
For the supercritical contact process on the hyper-cubic lattice started from a single infection at the origin and conditioned on survival, we establish two uniformity results for the hitting times $t(x)$, defined for each site $x$ as the…
For stochastic processes leading to condensation, the condensate, once it is formed, performs an ergodic stationary-state motion over the system. We analyse this motion, and especially its characteristic time, for zero-range processes. The…
In a coalescing random walk, a set of particles make independent random walks on a graph. Whenever one or more particles meet at a vertex, they unite to form a single particle, which then continues the random walk through the graph.…
We study continuous time Markov processes on graphs. The notion of frequency is introduced, which serves well as a scaling factor between any Markov time of a continuous time Markov process and that of its jump chain. As an application, we…
Inspired by strict-monotonicity criteria for the time constant in first passage percolation, we investigate convex ordering of point processes in relation to the time constant in first contact percolation. In a nutshell, first contact…
We study the extinction of epidemics in a generalized susceptible-infected-susceptible model, where a susceptible individual becomes infected with the rate $\lambda$ when contacting $m$ infective individual(s) simultaneously, and an…
We study the mixing time of the averaging process on a large random $d$-regular graph, $d\ge 3$, and prove an $L^2$-cutoff with an explicit cutoff time. Somewhat surprisingly, we uncover a phase transition at the finite, fixed degree…
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 ($1 \longrightarrow 0$)…
Motivated by stability questions on piecewise deterministic Markov models of bacterial chemotaxis, we study the long time behavior of a variant of the classic telegraph process having a non-constant jump rate that induces a drift towards…
We study diffusion processes in $\mathbb{R}^d$ that leave invariant a finite collection of manifolds (surfaces or points) in $\mathbb{R}^d$ and small perturbations of such processes. Assuming certain ergodic properties at and near the…
We investigate the macroscopic time evolution and stationary states of a mean field generalized contact process in $\mathbb{R}^d$. The model is described by a coupled set of nonlinear integral-differential equations. It was inspired by a…
We define a general model of stochastically-evolving graphs, namely the \emph{Edge-Uniform Stochastically-Evolving Graphs}. In this model, each possible edge of an underlying general static graph evolves independently being either alive or…
Reachability and other path-based measures on temporal graphs can be used to understand spread of infection, information, and people in modelled systems. Due to delays and errors in reporting, temporal graphs derived from data are unlikely…
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…
Disease control is of paramount importance in public health with infectious disease extinction as the ultimate goal. Although diseases may go extinct due to random loss of effective contacts where the infection is transmitted to new…