Graph Construction: Martingales & Polynomials

This lecture delves into the construction of graphs by adding multiple edges in sequence, focusing on the concept of martingales. The instructor explains the process of forming a Doob martingale and its application in constructing polynomials. By exploring the relationship between polynomials and eigenvalues, the lecture demonstrates how martingales can be used to find extreme polynomials and solve eigenvalue problems with low probability possibilities.