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arXiv · 2603.25622

The Geometry of Efficient Nonconvex Sampling

Santosh S. Vempala·Andre Wibisono
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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 $\mathcal{X}$.

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Santosh S. Vempala, Andre Wibisono. 2026-03-26. The Geometry of Efficient Nonconvex Sampling. https://arxiv.org/abs/2603.25622

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