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Probability and Dynamical Systems Seminar
Probability and Dynamical Systems Seminar
The frog model on transitive graphs
The frog model on transitive graphs
Organizers
Speaker
Yuliang Shi
Time
Tuesday, October 13, 2026 3:15 PM - 4:15 PM
Venue
A3-3-301
Online
Zoom 482 240 1589
(BIMSA)
Abstract
The frog model describes the spread of infection on a graph. Vertices initially contain independent Poisson numbers of particles with a common mean, the particle density. Only particles at the origin are initially active. Once activated, particles perform independent random walks, awakening sleeping particles along the way, and are removed when their lifespans end.
This talk concerns extinction–survival phase transitions in lifespan and particle density. I will briefly discuss the existence of such transitions on vertex-transitive graphs, then focus on sharpness. A key idea of our sharpness proof is to identify a frog-model analog of the percolation quantity introduced by Duminil-Copin and Tassion in 2015: the expected number of open boundary edges whose inner endpoints are connected to the origin within a finite set. I will explain how this quantity is used in our proof.
This talk concerns extinction–survival phase transitions in lifespan and particle density. I will briefly discuss the existence of such transitions on vertex-transitive graphs, then focus on sharpness. A key idea of our sharpness proof is to identify a frog-model analog of the percolation quantity introduced by Duminil-Copin and Tassion in 2015: the expected number of open boundary edges whose inner endpoints are connected to the origin within a finite set. I will explain how this quantity is used in our proof.
Speaker Intro
Yuliang Shi is a PhD student in mathematics at the University of British Columbia, supervised by Omer Angel and Jonathan Hermon.