  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 wake-up time, i.e. 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 weighted sum of geometric
random variables. This project was part of the University of Washington
Research Experience for Undergraduates program.

Probability