Numerical Estimation of Several Topological Quantities of the First Passage Percolation Model

Dissertation Defense
Monday, April 5, 2021 - 1:00pm for 2 hours
Yuanzhe Ma – Georgia Institute of Technology –
Michael Damron

In this thesis, our main goal is to use numerical simulations to study some quantities related to the growing set B(t). Motivated by prior works, we mainly study quantities including the boundary size, the hole size, and the location of each hole for B(t). We discuss the theoretical background of this work, the algorithm we used to conduct simulations, and include an extensive discussion of our simulation results. Our results support some of the prior conjectures and further introduce several interesting open problems.

This defense will be conducted on bluejeans, at