Free Central Limit Theorem, Semicircular Element, and Dyck Paths
Date:
I worked with undergraduate student Yujun Che and received guidance from graduate student Sam McKeown. We primarily used the book Lectures on the Combinatorics of Free Probability.
Free probability applies ideas from probability to abstract settings where variables may not commute. In these settings, expectations and distributions still provide useful structure and connect naturally to random matrix theory. This project focused on the free central limit theorem, semicircular elements, and Dyck paths through the combinatorial viewpoint of free probability.