Consider an interacting particle system indexed by the vertices of a (possibly random)
locally finite graph whose vertices and edges are equipped with weights or marks that …

Large ensembles of stochastically evolving interacting particles describe phenomena in
diverse fields including statistical physics, neuroscience, biology, and engineering. In such …

We find a non-trivial phase transition for the contact process, a simple model for infection
without immunity, on a network which reacts dynamically to prevent an epidemic. This …

Information diffusion models on networks are at the forefront of AI research. The dynamics of
such models typically follow stochastic models from epidemiology, used to model not only …

We analyze the Susceptible-Infected-Recovered-Susceptible (SIRS) process, a continuous-
time Markov chain frequently employed in epidemiology to model the spread of infections on …

We study the contact process on random graphs with low infection rate λ. For random d-
regular graphs, it is known that the survival time is O (log⁡ n) below the critical λ c. By …

The SIS model is a classic model from epidemiology that formalizes a variety of diffusion
processes on networks, such as biological infections and information dissemination. In this …

Diffusion of information in networks is at the core of many problems in AI. Common
examples include the spread of ideas and rumors as well as marketing campaigns …

We study the SIRS process—a continuous-time Markov chain modeling the spread of
infections on graphs. In this model, vertices are either susceptible, infected, or recovered …

We study the survival/extinction phase transition for contact processes with quenched
disorder. The disorder is given by a locally finite random graph with vertices indexed by the …