Some of the fastest ways to draw samples from a complicated probability distribution share a known flaw: they are biased, meaning they systematically miss the true target by a little. The usual fix, a Metropolis-Hastings accept-reject step, removes the bias but forces tiny step sizes, which makes everything slow. So it helps to know when you can just live with the bias.

This paper extends a reassuring result to two popular unadjusted samplers. The rough message: the bias is 'delocalized', spread thinly across all the dimensions, so if you only care about a handful of variables at a time, the error you actually feel stays small. Concretely, controlling the error on any K of the variables takes only about the square root of K integration steps, as long as the variables interact weakly or sparsely.

This is a plain gloss of a technical abstract, so the paper holds the precise assumptions and bounds.