4 papers · 1 filter
Fréchet Means in Infinite Dimensions
Adam Quinn Jaffe
While there exists a well-developed asymptotic theory of Fréchet means of random variables taking values in a general "finite-dimensional" metric space, there are only a few known…
Coupling Theory, Optimal Transport, and Strassen's Theorem for Eventual Domination
Adam Quinn Jaffe, Daniel Raban
Many results in probability (most famously, Strassen's theorem on stochastic domination), characterize some relationship between probability distributions in terms of the existence…
A Strong Duality Principle for Equivalence Couplings and Total Variation
Adam Quinn Jaffe
We introduce and study a notion of duality for two classes of optimization problems commonly occurring in probability theory. That is, on an abstract measurable space $(Ω,\mathcal…
Large Deviations Principle for Bures-Wasserstein Barycenters
Adam Quinn Jaffe, Leonardo V. Santoro
We prove the large deviations principle for empirical Bures-Wasserstein barycenters of independent, identically-distributed samples of covariance matrices and covariance operators.…