Frog model wakeup time on the complete graph
Probability
2015-10-21 v1
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.
Cite
@article{arxiv.1510.05995,
title = {Frog model wakeup time on the complete graph},
author = {Nikki Cartern and Brittany Dygert and Matthew Junge and Stephen Lacina and Collin Litterell and Austin Stromme and Andrew You},
journal= {arXiv preprint arXiv:1510.05995},
year = {2015}
}
Comments
9 pages