Frog model wakeup time on the complete graph
Nikki Cartern, Brittany Dygert, Matthew Junge, Stephen Lacina, Collin, Litterell, Austin Stromme, Andrew You

TL;DR
This paper analyzes the frog model on complete graphs, providing an elementary proof that the expected wake-up time scales as Theta(log n) and deriving an explicit distributional equation for it.
Contribution
It offers a new elementary proof for the wake-up time scaling and presents an explicit distributional equation for the wake-up time in the frog model.
Findings
Expected wake-up time is Theta(log n)
Derived an explicit distributional equation for wake-up time
Simplified understanding of the frog model on complete graphs
Abstract
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.
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Taxonomy
TopicsComplex Network Analysis Techniques · Opinion Dynamics and Social Influence · Stochastic processes and statistical mechanics
