Daniel Lacker

Approximate independence of typical marginals of high-dimensional probability measures

For many probability measures on $\mathbb{R}^n$, and for $k$ sufficiently smaller than $n$, most $k$-dimensional coordinate marginals are close to product measures. We prove this in two regimes, which notably involve no exchangeability assumptions as in prior theorems of de Finetti type. First, for log-concave measures...