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arXiv · 1510.05995

Frog model wakeup time on the complete graph

Nikki Cartern·Brittany Dygert·Matthew Junge·Stephen Lacina·Collin Litterell·Austin Stromme·Andrew You
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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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Nikki Cartern, Brittany Dygert, Matthew Junge, Stephen Lacina, Collin Litterell, Austin Stromme, Andrew You. 2015-10-20. Frog model wakeup time on the complete graph. https://arxiv.org/abs/1510.05995

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