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  "path": "/abs/2603.25622v1",
  "publishedAt": "2026-03-27T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Santosh S. Vempala",
    "Andre Wibisono"
  ],
  "textContent": "**Authors:** Santosh S. Vempala, Andre Wibisono\n\nWe 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 $\\mathcal{X}$.",
  "title": "The Geometry of Efficient Nonconvex Sampling"
}