Percolation Theory: Exploring Thresholds in Random Graphs by Daniel Zhang & Kevin Zhuo ’25

Percolation Theory: Exploring Thresholds in Random Graphs by Daniel Zhang & Kevin Zhuo ’25, Monday February 17, 1:00 – 1:50pm, North Science Building 113, Wachenheim, Mathematics Colloquium

Abstract: Imagine pouring some quantity of water into a bucket of soil. What is the probability that the water “percolates” across the entire bucket of soil? Percolation theory transforms this practical example into an exploration of the behavior of random graphs. This talk will introduce the fundamental concepts of random graphs and percolation. Then, we will prove the existence of a percolation threshold in a two-dimensional lattice and examine its properties.