The frog model on trees
Time and place
12:30 PM on Thursday, September 13th, 2018; NAC 6/114
Tobias Johnson (College of Staten Island (CUNY))
Abstract
Imagine that every vertex of a graph contains a sleeping frog. At time 0, the frog at one vertex wakes up and begins a random walk. When it moves to a new vertex, the sleeping frog there wakes up and begins its own random walk, which in turn wakes up any sleeping frogs it lands on, and so on. This process is called the frog model, and despite the cutesy name, it's a serious object of study for which many basic questions remain open.
I'll talk about the frog model on trees, where the model displays some interesting phase transitions. In particular, I'll (mostly) answer a question posed by Serguei Popov in 2003 by showing that on a binary tree, all frogs wake up with probability one, while on a 5-ary or higher tree, some frogs remain asleep forever with probability one. This is joint work with Christopher Hoffman and Matthew Junge.
