A Separation in Heavy-Tailed Sampling: Gaussian vs. Stable Oracles for Proximal Samplers

We study the complexity of heavy-tailed sampling and present a separation result in terms of obtaining high-accuracy versus low-accuracy guarantees i.e., samplers that require only O(log(1/ε)) versus Ω(poly(1/ε)) iterations to output a sample which is ε-close to the target in χ