The frog model is a system of random walks where active particles set sleeping particles in motion. On the complete graph with n vertices it is equivalent to a well-understood rumor spreading model. We given an alternate and elementary proof that the wakeup time, that is, the expected time for every particle to be activated, is &Theta(log n). Additionally, we give an explicit distributional equation for the wakeup time as a mixture of geometric random variables.
Matthew Junge, University of Washington
Carter, Nikki; Dygert, Brittany; Lacina, Stephen; Litterell, Collin; Stromme, Austin; and You, Andrew
"Frog Model Wakeup Time on the Complete Graph,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 17
, Article 9.
Available at: https://scholar.rose-hulman.edu/rhumj/vol17/iss2/9