arXiv:2603.25622v1 Announce Type: cross
Abstract: We present an efficient algorithm for uniformly sampling from an arbitrary compact body $mathcal{X} subset mathbb{R}^n$ from a warm start under isoperimetry and a natural volume growth condition. Our result provides a substantial common generalization of known results for convex bodies and star-shaped bodies. The complexity of the algorithm is polynomial in the dimension, the Poincar’e constant of the uniform distribution on $mathcal{X}$ and the volume growth constant of the set $mathcal{X}$.