5 papers
On quasi-stationary distributions for stochastic rumor models
Iddo Ben-Ari, Elcio Lebensztayn, Lucas Sousa Santos
This paper examines the quasi-stationary behavior of stochastic rumor processes. Using the results by van Doorn and Pollett (2008), we first prove that the continuous-time Maki--Th…
The maximum proportion of spreaders in stochastic rumor models
Elcio Lebensztayn, Pablo M. Rodriguez
We examine a general stochastic rumor model characterized by specific parameters that govern the interaction rates among individuals. Our model includes the \((α, p)\)-probability…
Laws of large numbers for the frog model on the complete graph
Elcio Lebensztayn, Mario Andres Estrada
The frog model is a stochastic model for the spreading of an epidemic on a graph, in which a dormant particle starts to perform a simple random walk on the graph and to awake other…
A new upper bound for the critical probability of the frog model on homogeneous trees
Elcio Lebensztayn, Jaime Utria
We consider the interacting particle system on the homogeneous tree of degree , known as frog model. In this model, active particles perform independent random walks, awak…
Phase transition for the frog model on biregular trees
Elcio Lebensztayn, Jaime Utria
We study the frog model with death on the biregular tree . Initially, there is a random number of awake and sleeping particles located on the vertices of the…