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Kyle Luh

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Martingale Couplings and Bounds on Tails of Probability Distributions

Nicholas Pippenger
Second Reader(s)
Francis Edward Su


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.


Asymptotic Bounds on the Hypergeometric Distribution

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