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 Poincaré constant of the uniform distribution on $\mathcal{X}$ and the volume growth constant of the set $\mathcal{X}$.

翻译：我们提出了一种高效算法，用于在等周性质及自然体积增长条件下，从任意紧致体 $\mathcal{X} \subset \mathbb{R}^n$ 中借助热启动进行均匀采样。该结果提供了凸体与星形体已知结果的重要统一推广。算法复杂度与维度、$\mathcal{X}$ 上均匀分布的庞加莱常数以及集合 $\mathcal{X}$ 的体积增长常数均呈多项式关系。