Date of Award

Summer 8-22-2025

Level of Access Assigned by Author

Open-Access Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

First Committee Advisor

Brandon Hanson

Second Committee Member

Jane Wang

Third Committee Member

Neel Patel

Abstract

In this thesis, we seek to understand the use of entropy and other information theoretic tools and their application in understanding the sum entropy H(X + Y ) of random variables X, Y taking values on the boolean cube {0, 1} d . Motivated by work of Kane and Tao, who provided an upper bound for the additive energy of subsets of the cube, we prove a lower bound for the sum entropy in terms of the individual entropies H(X) and H(Y ). In addition, we completely classify which random variables achieve the lower bound. We discuss further how a stability result for the entropy inequality could be developed

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