Kyle Luh
Thesis
Martingale Couplings and Bounds on Tails of Probability Distributions
- Advisor
- Nicholas Pippenger
- Second Reader(s)
- Francis 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
