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.

Author Bio

Nikki Carter, Brittany Dygert, Stephen Lacina, Collin Litterell, Austin Stromme, and Andrew You are all undergraduate students from across the country who participated in the 2015 Mathematics REU at the University of Washington. As part of their work, they collaborated on and coauthored this paper under the direction of the University of Washington Ph.D. candidate Matthew Junge.