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Kyle Luh

Picture of Kyle Luh.

Thesis

Martingale Couplings and Bounds on Tails of Probability Distributions

Advisor
Nicholas Pippenger
Second Reader(s)
Francis Edward Su

Abstract

Wassily Hoeffding, in his 1963 paper, introduces a procedure to derive inequalities between distributions. This method relies on finding a martingale coupling between the two random variables. I have developed a construction that establishes such couplings in various urn models. I use this construction to prove the inequality between the hypergeometric and binomial random variables that appears in Hoeffding's paper. I have then used and extended my urn construction to create new inequalities.

Proposal

Asymptotic Bounds on the Hypergeometric Distribution

Additional Materials

Poster