Variance bounds in product measures without exponential tails
We establish analogs of Cheeger's inequality for probability measures with heavy tails. As one of the principal applications, suppose $λ> 3$ and define the (Pareto) probability measure $μ_λ$ on $[1,\infty)$ by $dμ_λ(x) = (λ- 1) x^{-λ}$. Let $μ_λ^n$ denote the product measure of $μ_λ$ on $\mathbb{R}^n$. Then, for any $1$-Lipschitz...