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 Poincaré constant of the uniform distribution on $\mathcal{X}$ and the volume growth constant of the set $\mathcal{X}$.
From: Andre Wibisono [view email]
[v1]
Thu, 26 Mar 2026 16:35:53 UTC (820 KB)
[v2]
Tue, 30 Jun 2026 14:55:16 UTC (821 KB)
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